OVERZICHT FORMULES
Differentiëren
naam van de regel | functie | afgeleide |
somregel | $s(x)=f(x)+g(x) | $s^{\prime}(x)=f^{\prime}(x)+g^{\prime}(x) |
verschilregel | $v(x)=f(x)-g(x) | $v^{\prime}(x)=f^{\prime}(x)-g^{\prime}(x) |
productregel | $p(x)=f(x) \cdot g(x) | $p^{\prime}(x)=f^{\prime}(x) \cdot g(x)+f(x) \cdot g^{\prime}(x) |
quotiëntregel | $q(x)=\frac{f(x)}{g(x)} | $q^{\prime}(x)=\frac{f^{\prime}(x) \cdot g(x)-f(x) \cdot g^{\prime}(x)}{(g(x))^{2}} |
kettingregel | $k(x)=f(g(x)) | $k^{\prime}(x)=f^{\prime}(g(x)) \cdot g^{\prime}(x)of$\frac{\mathrm{d} k}{\mathrm{~d} x}=\frac{\mathrm{d} f}{\mathrm{~d} g} \cdot \frac{\mathrm{~d} g}{\mathrm{~d} x} |
Logaritmen
regel | voorwaarde |
${ }^{g} \log (a)+{ }^{g} \log (b)={ }^{g} \log (a b) | $g>0, g \neq 1, a>0, b>0 |
${ }^{g} \log (a)-{ }^{g} \log (b)={ }^{g} \log (\frac{a}{b}) | $g>0, g \neq 1, a>0, b>0 |
${ }^{g} \log (a^{p})=p \cdot{ }^{g} \log (a) | $g>0, g \neq 1, a>0 |
$g^{g} \log (a)=\frac{{ }^{p} \log (a)}{{ }^{p} \log (g)} | $g>0, g \neq 1, a>0, p>0, p \neq 1 |