De afgeleide van f(x)=ax^n voor elke 𝑛 van R

Afgeleide van f(x)=\sqrt{x}f(x)=\sqrt{\placeholder{}}f(x)=f(x)=\surd

Laten we beginnen met de functief(x)=\sqrt{x}f(x)=\surd\sqrt{x}f(x)=\surd\sqrt{x}xf(x)=\surd\sqrt{x0}xf(x)=\surd\sqrt{x}xf(x)=\surd\sqrt{\placeholder{}}x. Op het eerste gezicht lijkt deze functie niet van de vorm , maar we kunnen \sqrt{x}\sqrt{\placeholder{}}\frac{}{\placeholder{}}\frac{w}{\placeholder{}}\frac{wp}{\placeholder{}}\frac{w}{\placeholder{}}\frac{\placeholder{}}{\placeholder{}}wwow\surdherschrijven alsx^{\frac12}\left.x^{\frac12}\right)\left(x^{\frac12}\right)x^{\frac12})x^{\frac{1}{\placeholder{}}})x^1)\frac{x^1}{})\frac{x^1}{2})\frac{x^1}{\placeholder{}})x^1)x^{})x^{(})x^{(}2)x^{(}/2).

Stappen voor differentiatie:

•Herschrijven:f(x)=x^{\frac12}f(x)=x^{\frac{1}{\placeholder{}}}f(x)=x^1f(x)=x^{}f(x)=x^{(}f(x)=x^{(}1f(x)=x^{(}1/f(x)=x^{(}1/2

•Differentiëren: f^{\prime}\left(x\right)=\left(\frac12\right)\cdot x^{\left(\right.\frac12-1)}=\frac12x^{-\frac12}f^{\prime}\left(x\right)=\left(\frac12\right)\cdot x^{\left(\right.\frac12-1)}=\frac12x^{-\frac{1}{}}f^{\prime}\left(x\right)=\left(\frac12\right)\cdot x^{\left(\right.\frac12-1)}=\frac12x^{-\frac12}f^{\prime}\left(x\right)=\left(\frac12\right)\cdot x^{\left(\right.\frac12-1)}=\frac12x^{-\frac{1}{\placeholder{}}}f^{\prime}\left(x\right)=\left(\frac12\right)\cdot x^{\left(\right.\frac12-1)}=\frac12x^{-1}f^{\prime}\left(x\right)=\left(\frac12\right)\cdot x^{\left(\right.\frac12-1)}=\frac12x^{-}f^{\prime}\left(x\right)=\left(\frac12\right)\cdot x^{\left(\right.\frac12-1)}=\frac12xf^{\prime}\left(x\right)=\left(\frac12\right)\cdot x^{\left(\right.\frac12-1)}=\frac12f^{\prime}\left(x\right)=\left(\frac12\right)\cdot x^{\left(\right.\frac12-1)}=\frac{1}{\placeholder{}}f^{\prime}\left(x\right)=\left(\frac12\right)\cdot x^{\left(\right.\frac12-1)}=1f^{\prime}\left(x\right)=\left(\frac12\right)\cdot x^{\left(\right.\frac12-1)}=f^{\prime}\left(x\right)=\left(\frac12\right)\cdot x^{\left(\right.\frac12-1)}f^{\prime}\left(x\right)=\left(\frac12\right)\cdot x^{\left(\right)\frac12-1)}f^{\prime}\left(x\right)=\left(\frac12\right)\cdot x^{\left(\right)\frac12-1}f^{\prime}\left(x\right)=\left(\frac12\right)\cdot x^{\frac12-1}f^{\prime}\left(x\right)=\left(\frac12\right)\cdot x\left(\right.^{\frac12-1}f^{\prime}\left(x\right)=\left(\frac12\right)\cdot x\left(\right.^{\frac12-1}f^{\prime}\left(x\right)=\left(\frac12\right)\cdot x\left(\right.^{\frac12-1})f^{\prime}\left(x\right)=\left(\frac12\right)\cdot x\left(\right)^{\frac12-1})f^{\prime}\left(x\right)=\left(\frac12\right)\cdot x\left(\right)^{\frac12-1}f^{\prime}\left(x\right)=\left(\frac12\right)\cdot x^{\frac12-1}f^{\prime}x)=\left(\frac12\right)\cdot x^{\frac12-1}f^{\prime}x=\left(\frac12\right)\cdot x^{\frac12-1}f^{\prime}\left.x=\frac12\right)\cdot x^{\frac12-1}f^{\prime}\left.x=\left(\right.\frac12\right)\cdot x^{\frac12-1}f^{\prime}\left.x=\left(\right.\frac12\right)\cdot x^{\frac12-1}f^{\prime}\left.x)=\left(\right.\frac12\right)\cdot x^{\frac12-1}f^{\prime}\left(x)=\left(\right.\frac12\right)\cdot x^{\frac12-1}f^{\prime}\left.x)=\left(\right.\frac12\right)\cdot x^{\frac12-1}f^{\prime}\left(x)=\left(\right.\frac12\right)\cdot x^{\frac12-1}f^{\prime}\left(x)=\left(\right)\frac12\right)\cdot x^{\frac12-1}f^{\prime}\left(x)=\frac12\right)\cdot x^{\frac12-1}f^{\prime}(x)=\frac12\cdot x^{\frac12-1}f^{\prime}(x)=\frac12x^{\frac12-1}f^{\prime}(x)=\frac{1}{\placeholder{}}x^{\frac12-1}f^{\prime}(x)=1x^{\frac12-1}f^{\prime}(x)=x^{\frac12-1}f^{\prime}(x)=(x^{\frac12-1}f^{\prime}(x)=(1x^{\frac12-1}f^{\prime}(x)=(1/x^{\frac12-1}f^{\prime}(x)=(1/2x^{\frac12-1}f^{\prime}(x)=(1/2)x^{\frac12-1}f^{\prime}(x)=(1/2)*x^{\frac12-1}f^{\prime}(x)=(1/2)*x^{\frac12-}f^{\prime}(x)=(1/2)*x^{\frac12}f^{\prime}(x)=(1/2)*x^{\frac{1}{\placeholder{}}}f^{\prime}(x)=(1/2)*x^1f^{\prime}(x)=(1/2)*x^{}f^{\prime}(x)=(1/2)*x^{(}f^{\prime}(x)=(1/2)*x^{(}-f^{\prime}(x)=(1/2)*x^{(}-1f^{\prime}(x)=(1/2)*x^{(}-1/f^{\prime}(x)=(1/2)*x^{(}-1/2

•Omzetten naar breuken: Dit wordtf^{\prime}(x)=\frac{1}{2\sqrt{x}}f^{\prime}(x)=\frac{1}{2\sqrt{\placeholder{}}}f^{\prime}(x)=\frac12f^{\prime}(x)=\frac12(f^{\prime}(x)=\frac12(2f^{\prime}(x)=\frac12(2\surdf^{\prime}(x)=\frac12(2\surd xf^{\prime}(x)=\frac12(2\surd x)f^{\prime}(x)=\frac{1}{\placeholder{}}(2\surd x)f^{\prime}(x)=1(2\surd x)

Hieruit volgt dat de afgeleide van \sqrt{x}\sqrt{\placeholder{}}\surd gelijk is aan\frac{1}{2\sqrt{x}}\frac{1}{2\sqrt{\placeholder{}}}\frac12\frac{1}{}\frac12\frac{1}{\placeholder{}}1.1..1.1/.1/(.1/(2.1/(2\surd.1/(2\surd x.

Voorbeeld 1:f(x)=4x^3\cdot\sqrt{x}f(x)=4x^3\cdot\sqrt{\placeholder{}}f(x)=4x^3\cdotf(x)=4x^3\cdot xf(x)=4x^3\cdot\surd xf(x)=4x^3\surd x

Voor deze functie passen we dezelfde technieken toe.

Stappen voor differentiatie:

•Herschrijven:f(x)=4x^3\cdot x^{\frac12}=4x^{\left(^{}3+\frac12\right)}=4x^{3\frac12}f(x)=4x^3\cdot x^{\frac12}=4x^{\left(^{}3+\frac12\right)}=4x^{3=\frac12}f(x)=4x^3\cdot x^{\frac12}=4x^{\left(^{}3+\frac12\right)}=4x^{3=\frac{1}{\placeholder{}}}f(x)=4x^3\cdot x^{\frac12}=4x^{\left(^{}3+\frac12\right)}=4x^{3=1}f(x)=4x^3\cdot x^{\frac12}=4x^{\left(^{}3+\frac12\right)}=4x^{3=}f(x)=4x^3\cdot x^{\frac12}=4x^{\left(^{}3+\frac12\right)}=4x^3f(x)=4x^3\cdot x^{\frac12}=4x^{\left(^{}3+\frac12\right)}=4x^31f(x)=4x^3\cdot x^{\frac12}=4x^{\left(^{}3+\frac12\right)}=4x^3f(x)=4x^3\cdot x^{\frac12}=4x^{\left(^{}3+\frac12\right)}=4x^{}f(x)=4x^3\cdot x^{\frac12}=4x^{\left(^{}3+\frac12\right)}=4x^{(}f(x)=4x^3\cdot x^{\frac12}=4x^{\left(^{}3+\frac12\right)}=4x^{(}3f(x)=4x^3\cdot x^{\frac12}=4x^{\left(^{}3+\frac12\right)}=4x^{(}3.f(x)=4x^3\cdot x^{\frac12}=4x^{\left(^{}3+\frac12\right)}=4x^{(}3.5f(x)=4x^3\cdot x^{\frac12}=4x^{\left(^{}3+\frac12\right)}=4x^{(}3.5)f(x)=4x^3\cdot x^{\frac12}=4x^{\left(^{}3+\frac12\right)}3=4x^{(}3.5)f(x)=4x^3\cdot x^{\frac12}=4x^{\left(^{}3+\frac12\right)}3)=4x^{(}3.5)f(x)=4x^3\cdot x^{\frac12}=4x^{\left(^{}3+\frac12\right)}32)=4x^{(}3.5)f(x)=4x^3\cdot x^{\frac12}=4x^{\left(^{}3+\frac12\right)}3/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{\frac12}=4x^{\left(^{}3+\frac12\right)}31/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{\frac12}=4x^{\left(^{}3+\frac12\right)}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{\frac12}=4x^{^{}3+\frac12)}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{\frac12}=4x^{^{}3+\frac12}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{\frac12}=4x^{^{}3+\frac{1}{\placeholder{}}}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{\frac12}=4x^{^{}3+1}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{\frac12}=4x^{^{}3+}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{\frac12}=4x^{^{}3}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{\frac12}=4x^{^{}3=}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{\frac12}=4x^{^{}3}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{\frac12}=4x^{^{}3=}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{\frac12}=4x^{^{}3}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{\frac12}=4x^{^{}3=}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{\frac12}=4x^{^{}3}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{\frac12}=4x^{^{}}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{\frac12}=4x^{^{v}}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{\frac12}=4x^{}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{\frac12}=4x^{(}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{\frac{1}{\placeholder{}}}=4x^{(}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^1=4x^{(}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{}=4x^{(}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{}1=4x^{(}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{}1/=4x^{(}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{}1/2=4x^{(}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{}1/2)=4x^{(}3+1/2)=4x^{(}3.5)f(x)=4x^3\cdot x^{(}1/2)=4x^{(}3+1/2)=4x^{(}3.5)f(x)=4x^3x^{(}1/2)=4x^{(}3+1/2)=4x^{(}3.5)

•Differentiëren: f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-1}=14x^{2\frac12}f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-1}=14x^{2-\frac12}f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-1}=14x^{2-\frac{1}{\placeholder{}}}f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-1}=14x^{2-1}f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-1}=14x^{2-}f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-1}=14x^2f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-1}=14x^20f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-1}=14x^2f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-1}=14x^2=f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-1}=14x^2f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-1}=14x^{}f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-1}=14x^2f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-1}=14x^{21}f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-1}=14x^2f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-1}=14x^{}f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-1}=14x^{^{}}f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-1}=14x^{^2}f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-1}=14x^{}f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-1}=14x^{(}f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-1}=14x^{(}2f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-1}=14x^{(}2.f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-1}=14x^{(}2.5f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-1}=14x^{(}2.5)f^{\prime}(x)=4\cdot3\frac12x^{3\frac12-}=14x^{(}2.5)f^{\prime}(x)=4\cdot3\frac12x^{3\frac12}=14x^{(}2.5)f^{\prime}(x)=4\cdot3\frac12x^{3=\frac12}=14x^{(}2.5)f^{\prime}(x)=4\cdot3\frac12x^{3=\frac{1}{\placeholder{}}}=14x^{(}2.5)f^{\prime}(x)=4\cdot3\frac12x^{3=1}=14x^{(}2.5)f^{\prime}(x)=4\cdot3\frac12x^{3=}=14x^{(}2.5)f^{\prime}(x)=4\cdot3\frac12x^3=14x^{(}2.5)f^{\prime}(x)=4\cdot3\frac12x^{}=14x^{(}2.5)f^{\prime}(x)=4\cdot3\frac12x^{b}=14x^{(}2.5)f^{\prime}(x)=4\cdot3\frac12x=14x^{(}2.5)f^{\prime}(x)=4\cdot3\frac12x^{}=14x^{(}2.5)f^{\prime}(x)=4\cdot3\frac12x^{(}=14x^{(}2.5)f^{\prime}(x)=4\cdot3\frac12x^{(}2=14x^{(}2.5)f^{\prime}(x)=4\cdot3\frac12x^{(}2.=14x^{(}2.5)f^{\prime}(x)=4\cdot3\frac12x^{(}2.)=14x^{(}2.5)f^{\prime}(x)=4\cdot3\frac12x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=4\cdot3\frac12x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=4\cdot3\frac12x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=4\cdot3\frac12x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=4\cdot3\frac12x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=4\cdot3\frac12x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=4\cdot3\frac12x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=4\cdot3-\frac12x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=4\cdot3-\frac{1}{\placeholder{}}x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=4\cdot3-1x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=4\cdot3-x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=4\cdot3x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=4\cdot3x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=4\cdot3=x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=4\cdot3x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=4\cdot3.x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=4\cdot3.=x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=4\cdot3.=1x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=4\cdot3.=x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=4\cdot3.x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=4\cdot3.5x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=4\cdot3.5\cdot x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=4\cdot3.5x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=4\cdot3.5*x^{(}2.5)=14x^{(}2.5)f^{\prime}(x)=43.5*x^{(}2.5)=14x^{(}2.5)

•Herschrijven van de exponent: f^{\prime}(x)=14x^2\cdot\sqrt{x}f^{\prime}(x)=14x^2\cdot\sqrt{\placeholder{}}f^{\prime}(x)=14x^2\cdotf^{\prime}(x)=14x^2\cdot\surdf^{\prime}(x)=14x^2\cdot\surd xf^{\prime}(x)=14x^2\surd x

Hieruit volgt dat de afgeleide van 4x^3\cdot\sqrt{x}4x^3\cdot\sqrt{\placeholder{}}4x^3\cdot4x^34x^3*4x^3*\surd gelijk is aan 14x^2\cdot\sqrt{x}14x^2\cdot\sqrt{\placeholder{}}14x^2\cdot14x^214x^2*14x^2*\surd14x^2*\surd x

Voorbeeld 2:g(x)=2x^5\cdot\sqrt[5]{x}g(x)=2x^5\cdot\sqrt{x}g(x)=2x^5\cdot\sqrt[3]{x}g(x)=2x^5\cdot\sqrt[3]{\placeholder{}}g(x)=2x^5\cdot\sqrt[3x]{\placeholder{}}g(x)=2x^5\cdot\sqrt[3]{\placeholder{}}g(x)=2x^5\cdot\sqrt[\placeholder{}]{\placeholder{}}g(x)=2x^5\cdotg(x)=2x^5g(x)=2x^5*g(x)=2x^5*∛

In dit voorbeeld moeten we de functie ook weer naar de juiste vorm brengen.

Stappen voor differentiatie:

•Herschrijven:g(x)=2x^5\cdot x^{\frac15}=2x^{5+\frac15}=2x^{5\frac15}g(x)=2x^5\cdot x^{\frac15}=2x^{5+\frac15}=2x^{\frac15}g(x)=2x^5\cdot x^{\frac15}=2x^{5+\frac15}=2x^{\frac{16}{5}}g(x)=2x^5\cdot x^{\frac15}=2x^{5+\frac15}=2x^{\frac{16}{}}g(x)=2x^5\cdot x^{\frac15}=2x^{5+\frac15}=2x^{\frac{16}{3}}g(x)=2x^5\cdot x^{\frac15}=2x^{5+\frac{1}{}}=2x^{\frac{16}{3}}g(x)=2x^5\cdot x^{\frac15}=2x^{5+\frac13}=2x^{\frac{16}{3}}g(x)=2x^5\cdot x^{\frac{1}{}}=2x^{5+\frac13}=2x^{\frac{16}{3}}g(x)=2x^5\cdot x^{\frac13}=2x^{5+\frac13}=2x^{\frac{16}{3}}g(x)=2x^5\cdot x^{\frac13}=2x^{5+\frac13}=2x^{\frac{16}{\placeholder{}}}g(x)=2x^5\cdot x^{\frac13}=2x^{5+\frac13}=2x^{16}g(x)=2x^5\cdot x^{\frac13}=2x^{5+\frac13}=2x^1g(x)=2x^5\cdot x^{\frac13}=2x^{5+\frac13}=2x^16g(x)=2x^5\cdot x^{\frac13}=2x^{5+\frac13}=2x^1g(x)=2x^5\cdot x^{\frac13}=2x^{5+\frac13}=2x^{}g(x)=2x^5\cdot x^{\frac13}=2x^{5+\frac13}=2x^{(}g(x)=2x^5\cdot x^{\frac13}=2x^{5+\frac13}=2x^{(}1g(x)=2x^5\cdot x^{\frac13}=2x^{5+\frac13}=2x^{(}16g(x)=2x^5\cdot x^{\frac13}=2x^{5+\frac13}=2x^{(}16/g(x)=2x^5\cdot x^{\frac13}=2x^{5+\frac13}=2x^{(}16/3g(x)=2x^5\cdot x^{\frac13}=2x^{5+\frac13}=2x^{(}16/3)g(x)=2x^5\cdot x^{\frac13}=2x^{5+\frac13}=2x^{(}16/3)g(x)=2x^5\cdot x^{\frac13}=2x^{5+\frac13}=2x^{(}16/3)g(x)=2x^5\cdot x^{\frac13}=2x^{5+\frac{1}{}}=2x^{(}16/3)g(x)=2x^5\cdot x^{\frac13}=2x^{5+\frac12}=2x^{(}16/3)g(x)=2x^5\cdot x^{\frac13}=2x^{5+\frac{1}{\placeholder{}}}=2x^{(}16/3)g(x)=2x^5\cdot x^{\frac13}=2x^{5+1}=2x^{(}16/3)g(x)=2x^5\cdot x^{\frac13}=2x^{5+}=2x^{(}16/3)g(x)=2x^5\cdot x^{\frac13}=2x^5=2x^{(}16/3)g(x)=2x^5\cdot x^{\frac13}=2x5+1/3=2x^{(}16/3)g(x)=2x^5\cdot x^{\frac13}=2x5+1/3)=2x^{(}16/3)g(x)=2x^5\cdot x^{\frac13}=2x^{}5+1/3)=2x^{(}16/3)g(x)=2x^5\cdot x^{\frac13}=2x^{(}5+1/3)=2x^{(}16/3)g(x)=2x^5\cdot x^{\frac{1}{\placeholder{}}}=2x^{(}5+1/3)=2x^{(}16/3)g(x)=2x^5\cdot x^1=2x^{(}5+1/3)=2x^{(}16/3)g(x)=2x^5\cdot x^{}=2x^{(}5+1/3)=2x^{(}16/3)g(x)=2x^5\cdot x^{(}=2x^{(}5+1/3)=2x^{(}16/3)g(x)=2x^5\cdot x^{(}1=2x^{(}5+1/3)=2x^{(}16/3)g(x)=2x^5\cdot x^{(}1/=2x^{(}5+1/3)=2x^{(}16/3)g(x)=2x^5\cdot x^{(}1/3=2x^{(}5+1/3)=2x^{(}16/3)g(x)=2x^5\cdot x^{(}1/3)=2x^{(}5+1/3)=2x^{(}16/3)g(x)=2x^5x^{(}1/3)=2x^{(}5+1/3)=2x^{(}16/3)

•Differentiëren: g^{\prime}(x)=2\cdot5\frac15\cdot x^{5\frac15-1}=10\frac25x^{4\frac15}g^{\prime}(x)=2\cdot5\frac15\cdot x^{5\frac15-1}=10\frac{}{5}x^{4\frac15}g^{\prime}(x)=2\cdot5\frac15\cdot x^{5\frac15-1}=10\frac15x^{4\frac15}g^{\prime}(x)=2\cdot5\frac15\cdot x^{5\frac15-1}=10\frac15x^{\frac15}g^{\prime}(x)=2\cdot5\frac15\cdot x^{5\frac15-1}=10\frac15x^{\frac{}{5}}g^{\prime}(x)=2\cdot5\frac15\cdot x^{5\frac15-1}=10\frac15x^{\frac15}g^{\prime}(x)=2\cdot5\frac15\cdot x^{5\frac15-1}=10\frac15x^{\frac{13}{5}}g^{\prime}(x)=2\cdot5\frac15\cdot x^{5\frac15-1}=10\frac15x^{\frac{13}{}}g^{\prime}(x)=2\cdot5\frac15\cdot x^{5\frac15-1}=10\frac15x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac15\cdot x^{5\frac15-1}=1\frac15x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac15\cdot x^{5\frac15-1}=\frac15x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac15\cdot x^{5\frac15-1}=\frac{}{5}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac15\cdot x^{5\frac15-1}=\frac35x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac15\cdot x^{5\frac15-1}=\frac{32}{5}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac15\cdot x^{5\frac15-1}=\frac{32}{}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac15\cdot x^{5\frac15-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac{1}{}\cdot x^{5\frac15-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac11\cdot x^{5\frac15-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac{}{1}\cdot x^{5\frac15-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac51\cdot x^{5\frac15-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac51\cdot x^{5\frac{1}{}-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac51\cdot x^{5\frac11-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac51\cdot x^{5\frac{}{1}-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac51\cdot x^{5\frac51-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac51\cdot x^{\frac51-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac51\cdot x^{1\frac51-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac51\cdot x^{10\frac51-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac51\cdot x^{1\frac51-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac51\cdot x^{\frac51-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac51\cdot x^{\frac{}{1}-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac51\cdot x^{\frac11-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac51\cdot x^{\frac{16}{1}-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac51\cdot x^{\frac{16}{}-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot5\frac51\cdot x^{\frac{16}{3}-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot\frac51\cdot x^{\frac{16}{3}-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot\frac{}{1}\cdot x^{\frac{16}{3}-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot\frac11\cdot x^{\frac{16}{3}-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot\frac{10}{1}\cdot x^{\frac{16}{3}-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot\frac11\cdot x^{\frac{16}{3}-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot\frac{16}{1}\cdot x^{\frac{16}{3}-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot\frac{16}{}\cdot x^{\frac{16}{3}-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{3}-1}=\frac{32}{3}x^{\frac{13}{3}}g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{3}-1}=\frac{32}{3}x^{\frac{13}{\placeholder{}}}g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{3}-1}=\frac{32}{3}x^{13}g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{3}-1}=\frac{32}{3}x^1g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{3}-1}=\frac{32}{3}x^{}g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{3}-1}=\frac{32}{3}x^{}3g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{3}-1}=\frac{32}{3}x^{}13g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{3}-1}=\frac{32}{3}x^{}133g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{3}-1}=\frac{32}{3}x^{}13/3g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{3}-1}=\frac{32}{3}x^{(}13/3g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{3}-1}=\frac{32}{3}x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{3}-1}=\frac{32}{\placeholder{}}x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{3}-1}=32x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{3}-1}=3x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{3}-1}=x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{3}-1}=(x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{3}-1}=(3x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{3}-1}=(32x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{3}-1}=(32/x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{3}-1}=(32/3x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{3}-1}=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{3}-}=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{3}}=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{\frac{16}{\placeholder{}}}=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{16}=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^1=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{}=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{}1=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{}16=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{}16/=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{}16/3=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{}16/3-=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{}16/3-1=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{}16/3-1)=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{(}16/3-1)=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{(}16/3-1)=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{3}\cdot x^{(}16/3-1)=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot\frac{16}{\placeholder{}}\cdot x^{(}16/3-1)=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot16\cdot x^{(}16/3-1)=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot1\cdot x^{(}16/3-1)=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot\cdot x^{(}16/3-1)=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot(\cdot x^{(}16/3-1)=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot(1\cdot x^{(}16/3-1)=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot(16\cdot x^{(}16/3-1)=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot(16/\cdot x^{(}16/3-1)=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot(16/3\cdot x^{(}16/3-1)=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot(16/3)\cdot x^{(}16/3-1)=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot(16/3)x^{(}16/3-1)=(32/3)x^{(}13/3)g^{\prime}(x)=2\cdot(16/3)*x^{(}16/3-1)=(32/3)x^{(}13/3)g^{\prime}(x)=2(16/3)*x^{(}16/3-1)=(32/3)x^{(}13/3)

•Herschrijven van de exponent:g^{\prime}(x)=10\frac25x^4\cdot\sqrt[5]{x}g^{\prime}(x)=1\frac25x^4\cdot\sqrt[5]{x}g^{\prime}(x)=\frac25x^4\cdot\sqrt[5]{x}g^{\prime}(x)=\frac{32}{5}x^4\cdot\sqrt[5]{x}g^{\prime}(x)=\frac{32}{}x^4\cdot\sqrt[5]{x}g^{\prime}(x)=\frac{32}{3}x^4\cdot\sqrt[5]{x}g^{\prime}(x)=\frac{32}{3}x^4\cdot\sqrt{x}g^{\prime}(x)=\frac{32}{3}x^4\cdot\sqrt[3]{x}g^{\prime}(x)=\frac{32}{3}x^4\cdot\sqrt[3]{\placeholder{}}g^{\prime}(x)=\frac{32}{3}x^4\cdot\sqrt[3]{\placeholder{}}xg^{\prime}(x)=\frac{32}{3}x^4\cdot\sqrt[3]{\placeholder{}}g^{\prime}(x)=\frac{32}{3}x^4\cdot\sqrt[\placeholder{}]{\placeholder{}}g^{\prime}(x)=\frac{32}{3}x^4\cdotg^{\prime}(x)=\frac{32}{3}x^4g^{\prime}(x)=\frac{32}{3}x^4\cdotg^{\prime}(x)=\frac{32}{3}x^4\cdot∛g^{\prime}(x)=\frac{32}{3}x^4\cdot∛xg^{\prime}(x)=\frac{32}{3}x^4∛xg^{\prime}(x)=\frac{32}{3}x^4*∛xg^{\prime}(x)=\frac{32}{\placeholder{}}x^4*∛xg^{\prime}(x)=32x^4*∛xg^{\prime}(x)=3x^4*∛xg^{\prime}(x)=x^4*∛xg^{\prime}(x)=(x^4*∛xg^{\prime}(x)=(3x^4*∛xg^{\prime}(x)=(32x^4*∛xg^{\prime}(x)=(32/x^4*∛xg^{\prime}(x)=(32/3x^4*∛x

Hieruit volgt dat de afgeleide van 2x^5\cdot\sqrt[5]{x}2x^5\cdot\sqrt{x}2x^5\cdot\sqrt[3]{x}2x^5\cdot\sqrt[3]{\placeholder{}}2x^5\cdot\sqrt[3]{\placeholder{}}x2x^5\cdot\sqrt[3]{\placeholder{}}2x^5\cdot\sqrt[\placeholder{}]{\placeholder{}}2x^5\cdot2x^5\cdot∛2x^5\cdot∛x2x^5∛x gelijk is aan10\frac25x^4\cdot\sqrt[5]{x}.10\frac25x^4\cdot\sqrt{x}.10\frac25x^4\cdot\sqrt[3]{x}.10-\frac25x^4\cdot\sqrt[3]{x}.10-\frac{2}{\placeholder{}}x^4\cdot\sqrt[3]{x}.10-2x^4\cdot\sqrt[3]{x}.10-x^4\cdot\sqrt[3]{x}.10x^4\cdot\sqrt[3]{x}.1x^4\cdot\sqrt[3]{x}.x^4\cdot\sqrt[3]{x}.3x^4\cdot\sqrt[3]{x}.32x^4\cdot\sqrt[3]{x}.\frac{32}{}x^4\cdot\sqrt[3]{x}.\frac{32}{3}x^4\cdot\sqrt[3]{x}.\frac{32}{\placeholder{}}x^4\cdot\sqrt[3]{x}.32x^4\cdot\sqrt[3]{x}.3x^4\cdot\sqrt[3]{x}.x^4\cdot\sqrt[3]{x}.(x^4\cdot\sqrt[3]{x}.(3x^4\cdot\sqrt[3]{x}.(32x^4\cdot\sqrt[3]{x}.(32/x^4\cdot\sqrt[3]{x}.(32/3x^4\cdot\sqrt[3]{x}.(32/3)x^4\cdot\sqrt[3]{x}.(32/3)x^4\cdot\sqrt[3]{\placeholder{}}.(32/3)x^4\cdot\sqrt[\placeholder{}]{\placeholder{}}.(32/3)x^4\cdot.(32/3)x^4\cdot∛.(32/3)x^4\cdot∛x.(32/3)x^4∛x.

Voorbeeld 3: h(x)=\frac{6x-x^2}{2\sqrt[3]{x}}h(x)=\frac{6x-x^2)}{2\sqrt[3]{x}}h(x)=\frac{(6x-x^2)}{2\sqrt[3]{x}}h(x)=\frac{(6x-x^2)}{\sqrt[3]{x}}h(x)=\frac{(6x-x^2)}{\sqrt[3]{x}}/h(x)=\frac{(6x-x^2)}{\sqrt[3]{x}}/∛h(x)=\frac{(6x-x^2)}{\sqrt[3]{x}}/∛xh(x)=\frac{(6x-x^2)}{\sqrt[3]{\placeholder{}}}/∛xh(x)=\frac{(6x-x^2)}{\sqrt[\placeholder{}]{\placeholder{}}}/∛xh(x)=\frac{(6x-x^2)}{\placeholder{}}/∛x

Dit voorbeeld vereist enige extra stappen omdat we te maken hebben met een breuk.

Stappen voor differentiatie:

•Herschrijven van de noemer:\sqrt[3]{x}=x^{\frac{^1}{3}}\sqrt[3]{x}=x^{\frac{^1}{\placeholder{}}}\sqrt[3]{x}=x^{^1}\sqrt[3]{x}=x^{}\sqrt[3]{x}=x^{(}\sqrt[3]{x}=x^{(}1\sqrt[3]{x}=x^{(}1/\sqrt[3]{x}=x^{(}1/3\sqrt[3]{x}=x^{(}1/3)\sqrt[3]{\placeholder{}}=x^{(}1/3)\sqrt[\placeholder{}]{\placeholder{}}=x^{(}1/3)=x^{(}1/3)∛=x^{(}1/3)

•Afzonderen van termen: We verdelen elke term in de teller door de noemer. \frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x^{\frac23}-\frac12x^{1\frac23}\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x^{\frac23}-\frac12x^{1-\frac23}\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x^{\frac23}-\frac12x^{1-\frac{2}{\placeholder{}}}\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x^{\frac23}-\frac12x^{1-2}\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x^{\frac23}-\frac12x^{1-}\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x^{\frac23}-\frac12x^1\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x^{\frac23}-\frac12x^12\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x^{\frac23}-\frac12x^123\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x^{\frac23}-\frac12x^1\frac23\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x^{\frac23}-\frac12x^1-\frac23\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x^{\frac23}-\frac12x^1-\frac{2}{\placeholder{}}\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x^{\frac23}-\frac12x^1-2\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x^{\frac23}-\frac12x^1-\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x^{\frac23}-\frac12x^1\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x^{\frac23}-\frac12x\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x^{\frac23}-\frac12\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x^{\frac23}-\frac{1}{\placeholder{}}\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x^{\frac23}-1\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x^{\frac23}-\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x^{\frac23}\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x^{\frac{2}{\placeholder{}}}\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x^2\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=\frac{3x^2}{}\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=\frac{3x^2}{3}\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=\frac{3x^2}{\placeholder{}}\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x^2\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3x\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=x\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{}\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^3x\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^3x\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{}\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{}\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^{}\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/x\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/x)\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/x)=\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/x)=-\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/x)=-x\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/x)=-x^{}\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/x)=-x^{(}\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/x)=-x^{(}2\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/x)=-x^{(}2-\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/x)=-x^{(}2-1\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/x)=-x^{(}2-1/\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/x)=-x^{(}2-1/3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/x)=-x^{(}2-1/3)\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/x)=-x^{(}2-1/3)\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/x)=-x^{(}2-1/3)=\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/x)=-x^{(}2-1/3)=-\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/x)=-x^{(}2-1/3)=-x\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/x)=-x^{(}2-1/3)=-x^{}\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/x)=-x^{(}2-1/3)=-x^{(}\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/x)=-x^{(}2-1/3)=-x^{(}5\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/x)=-x^{(}2-1/3)=-x^{(}5/\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/(x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}11/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac13}}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^{\frac{1}{\placeholder{}}}}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x^1}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2x}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{2}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-\frac{x^2}{\placeholder{}}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-x^2=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-x=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}-=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x-x^2}{2\sqrt[3]{x}}=\frac{6x}{2x^{\frac13}}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x-x^2}{2\sqrt[3]{\placeholder{}}}=\frac{6x}{2x^{\frac13}}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x-x^2}{2\sqrt[\placeholder{}]{\placeholder{}}}=\frac{6x}{2x^{\frac13}}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x-x^2}{2}=\frac{6x}{2x^{\frac13}}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x-x^2}{\placeholder{}}=\frac{6x}{2x^{\frac13}}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/36x-x^2=\frac{6x}{2x^{\frac13}}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/36x-\frac{x^2}{\placeholder{}}=\frac{6x}{2x^{\frac13}}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/36x-x^2=\frac{6x}{2x^{\frac13}}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/36x-x=\frac{6x}{2x^{\frac13}}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/36x-=\frac{6x}{2x^{\frac13}}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/36x=\frac{6x}{2x^{\frac13}}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/36=\frac{6x}{2x^{\frac13}}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3=\frac{6x}{2x^{\frac13}}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x}{2x^{\frac13}}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x}{2x^{\frac{1}{\placeholder{}}}}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x}{2x^1}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x}{2x}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x}{2x1}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x}{2x}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x}{2}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3\frac{6x}{\placeholder{}}=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/36x=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/36=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/36=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/36x=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/36x)=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/36x)/=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/36x)/(=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/36x)/(∛=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/36x)/(∛x=6x^{(}1-1/3)=6x^{(}2/3)(-x^2)/(∛x)=-x^{(}2-1/3)=-x^{(}5/3

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h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56x^{\frac23}=\frac{2}{\sqrt[3]{x}}-\frac56\sqrt[3]{x^2}h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56x^{\frac23}=\frac{2}{\sqrt[3]{x}}-\frac56\sqrt[3]{x}h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56x^{\frac23}=\frac{2}{\sqrt[3]{x}}-\frac56\sqrt[3]{\placeholder{}}h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56x^{\frac23}=\frac{2}{\sqrt[3]{x}}-\frac56\sqrt[\placeholder{}]{\placeholder{}}h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56x^{\frac23}=\frac{2}{\sqrt[3]{x}}-\frac56h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56x^{\frac23}=\frac{2}{\sqrt[3]{x}}-\frac{5}{\placeholder{}}h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56x^{\frac23}=\frac{2}{\sqrt[3]{x}}-\frac{\placeholder{}}{\placeholder{}}h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56x^{\frac23}=\frac{2}{\sqrt[3]{x}}-h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56x^{\frac23}=\frac{2}{\sqrt[3]{x}}h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56x^{\frac23}=\frac{2}{\sqrt[3]{\placeholder{}}}h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56x^{\frac23}=\frac{2}{\sqrt[\placeholder{}]{\placeholder{}}}h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56x^{\frac23}=\frac{2}{}h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56x^{\frac23}=\frac23h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56x^{\frac23}=\frac{2}{\placeholder{}}h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56x^{\frac23}=2h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56x^{\frac23}=h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56x^{\frac23}h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56x^{\frac{2}{\placeholder{}}}h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56x^2h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56\frac{x^2}{}h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56\frac{x^2}{3}h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56\frac{x^2}{\placeholder{}}h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56x^2h^{\prime}\left(x\right)=2x^{-\frac13}-\frac56xh^{\prime}\left(x\right)=2x^{-\frac13}-\frac56h^{\prime}\left(x\right)=2x^{-\frac13}-\frac{5}{\placeholder{}}h^{\prime}\left(x\right)=2x^{-\frac13}-5h^{\prime}\left(x\right)=2x^{-\frac13}-h^{\prime}\left(x\right)=2x^{-\frac13}h^{\prime}\left(x\right)=2x^{-\frac{1}{\placeholder{}}}h^{\prime}\left(x\right)=2x^{-1}h^{\prime}\left(x\right)=2x^{-}h^{\prime}\left(x\right)=2xh^{\prime}\left(x\right)=2h^{\prime}\left(x\right)=h^{\prime}\left(x\right)h\left(x\right)h\left((x\right)h\left((\right)h\left(\right)h

Hieruit volgt dat de afgeleide van h(x)=\frac{6x-x^2}{2\sqrt[3]{x}} gelijk is aan h^{\prime}\left(x\right)=\frac{2}{\sqrt[3]{x}}-\frac56\sqrt[3]{x^2}h^{\prime}\left(x\right)\frac{2}{\sqrt[3]{x}}-\frac56\sqrt[3]{x^2}h^{\prime}\left(\right)\frac{2}{\sqrt[3]{x}}-\frac56\sqrt[3]{x^2}h^{\prime}\left(\right)\frac{2}{\sqrt[3]{x}}-\frac56\sqrt[3]{x^2}xh^{\prime}\left(\right)\frac{2}{\sqrt[3]{x}}-\frac56\sqrt[3]{x^2}h^{\prime}\frac{2}{\sqrt[3]{x}}-\frac56\sqrt[3]{x^2}h^{\prime}9\frac{2}{\sqrt[3]{x}}-\frac56\sqrt[3]{x^2}h^{\prime}9x\frac{2}{\sqrt[3]{x}}-\frac56\sqrt[3]{x^2}h^{\prime}9\frac{2}{\sqrt[3]{x}}-\frac56\sqrt[3]{x^2}h^{\prime}\frac{2}{\sqrt[3]{x}}-\frac56\sqrt[3]{x^2}h^{\prime}\frac{2}{\sqrt[3]{x}}-\frac56\sqrt[3]{x^2}h\frac{2}{\sqrt[3]{x}}-\frac56\sqrt[3]{x^2}h\times\frac{2}{\sqrt[3]{x}}-\frac56\sqrt[3]{x^2}h\times x\frac{2}{\sqrt[3]{x}}-\frac56\sqrt[3]{x^2}h\times\frac{2}{\sqrt[3]{x}}-\frac56\sqrt[3]{x^2}h^{\prime}\frac{2}{\sqrt[3]{x}}-\frac56\sqrt[3]{x^2}h\frac{2}{\sqrt[3]{x}}-\frac56\sqrt[3]{x^2}\frac{2}{\sqrt[3]{x}}-\frac56\sqrt[3]{x^2}.