OVERZICHT FORMULES
Differentiëren
naam van de regel | functie | afgeleide |
|---|---|---|
somregel | s\left(x\right)=f\left(x\right)+g\left(x\right)s\left(x\right)=f\left(x\right)+g\left(x\right)s\left(x\right)=f\left(x\right)+g\left(\right)s\left(x\right)=f\left(x\right)+gs\left(x\right)=f\left(x\right)+s\left(x\right)=f\left(x\right)s\left(x\right)=f\left(x\right)s\left(x\right)=f\left(\right)s\left(x\right)=fs\left(x\right)=s\left(x\right)s\left(x\right)s\left(\right)s | s^{\prime}\left(x\right)=f^{\prime}\left(x\right)+g^{\prime}\left(x\right)s\left(x\right)=f^{\prime}\left(x\right)+g^{\prime}\left(x\right)s\left(x\right)=f\left(x\right)+g^{\prime}\left(x\right)s\left(x\right)=f\left(x\right)+g\left(x\right) |
verschilregel | v\left(x\right)=f\left(x\right)-g\left(x\right)v\left(x\right)=f\left(x\right)-g\left(x\right)v\left(x\right)=f\left(x\right)-g\left(x\right)v\left(x\right)=f\left(x\right)-g\left(\right)v\left(x\right)=f\left(x\right)-gv\left(x\right)=f\left(x\right)-v\left(x\right)=f\left(x\right)v\left(x\right)=f\left(x\right)v\left(x\right)=f\left(\right)v\left(x\right)=fv\left(x\right)=v\left(x\right)v\left(x\right)v\left(\right)v | v^{\prime}\left(x\right)=f^{\prime}\left(x\right)-g^{\prime}\left(x\right)v^{\prime}\left(x\right)=f^{\prime}\left(x\right)-g\left(x\right)v^{\prime}\left(x\right)=f\left(x\right)-g\left(x\right)v\left(x\right)=f\left(x\right)-g\left(x\right) |
productregel | p\left(x\right)=f\left(x\right)\cdot g\left(x\right)p\left(x\right)=f\left(x\right)\cdot g\left(x\right)p\left(x\right)=f\left(x\right)\cdot g\left(\right)p\left(x\right)=f\left(x\right)\cdot gp\left(x\right)=f\left(x\right)\cdotp\left(x\right)=f\left(x\right)p\left(x\right)=f\left(x\right)p\left(x\right)=f\left(\right)p\left(x\right)=fp\left(x\right)=p\left(x\right)p\left(x\right)p\left(\right)p | p^{\prime}\left(x\right)=f^{\prime}\left(x\right)\cdot g\left(x\right)+f\left(x\right)\cdot g^{\prime}\left(x\right)p^{\prime}\left(x\right)=f^{\prime}\left(x\right)\cdot g\left(x\right)+f\left(x\right)\cdot g^{\prime}\left(x\right)p^{\prime}\left(x\right)=f^{\prime}\left(x\right)\cdot g\left(x\right)+f\left(x\right)\cdot g^{\prime}\left(\right)p^{\prime}\left(x\right)=f^{\prime}\left(x\right)\cdot g\left(x\right)+f\left(x\right)\cdot g^{\prime}p^{\prime}\left(x\right)=f^{\prime}\left(x\right)\cdot g\left(x\right)+f\left(x\right)\cdot gp^{\prime}\left(x\right)=f^{\prime}\left(x\right)\cdot g\left(x\right)+f\left(x\right)\cdotp^{\prime}\left(x\right)=f^{\prime}\left(x\right)\cdot g\left(x\right)+f\left(x\right)p^{\prime}\left(x\right)=f^{\prime}\left(x\right)\cdot g\left(x\right)+f\left(x\right)p^{\prime}\left(x\right)=f^{\prime}\left(x\right)\cdot g\left(x\right)+f\left(\right)p^{\prime}\left(x\right)=f^{\prime}\left(x\right)\cdot g\left(x\right)+fp^{\prime}\left(x\right)=f^{\prime}\left(x\right)\cdot g\left(x\right)+p^{\prime}\left(x\right)=f^{\prime}\left(x\right)\cdot g\left(x\right)p^{\prime}\left(x\right)=f^{\prime}\left(x\right)\cdot g\left(x\right)p^{\prime}\left(x\right)=f^{\prime}\left(x\right)\cdot g\left(\right)p^{\prime}\left(x\right)=f^{\prime}\left(x\right)\cdot gp^{\prime}\left(x\right)=f^{\prime}\left(x\right)\cdotp^{\prime}\left(x\right)=f^{\prime}\left(x\right)p^{\prime}\left(x\right)=f^{\prime}\left(x\right)p^{\prime}\left(x\right)=f^{\prime}\left(\right)p^{\prime}\left(x\right)=f^{\prime}\left(X\right)p^{\prime}\left(x\right)=f^{\prime}\left(\right)p^{\prime}\left(x\right)=f^{\prime}p^{\prime}\left(x\right)=fp^{\prime}\left(x\right)=p^{\prime}\left(x\right)p^{\prime}\left(x\right)p^{\prime}\left(x_{}\right)p^{\prime}\left(x_{=}\right)p^{\prime}\left(x_{=f}\right)p^{\prime}\left(x_{=f^{}}\right)p^{\prime}\left(x_{=f^{\prime}}\right)p^{\prime}\left(x_{=f^{\prime}\left(\right.}\right)p^{\prime}\left(x_{=f^{\prime}\left(x\right.}\right)p^{\prime}\left(x_{=f^{\prime}\left(x\right)}\right)p^{\prime}\left(x_{=f^{\prime}\left(x\right)}\right)p^{\prime}\left(x_{=f^{\prime}\left(\right)}\right)p^{\prime}\left(x_{=f^{\prime}}\right)p^{\prime}\left(x_{=f}\right)p^{\prime}\left(x_{=}\right)p^{\prime}\left(x\right)p^{\prime}\left(\right)p^{\prime}p |
quotiëntregel | q\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}q\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}q\left(x\right)=\frac{f\left(x\right)}{g\left(\right)}q\left(x\right)=\frac{f\left(x\right)}{g}q\left(x\right)=\frac{f\left(x\right)}{\placeholder{}}q\left(x\right)=f\left(x\right)q\left(x\right)=f\left(x\right)q\left(x\right)=f\left(\right)q\left(x\right)=fq\left(x\right)=q\left(x\right)q\left(x\right)q\left(x\right)q\left(\right)qqq\left(\right.q\left(x\right.q\left(x\right)q\left(x\right)_{}q\left(x\right)_{=}q\left(x\right)q\left(x\right)q\left(\right)qqq\left(\right.q\left(x\right.q\left(x\right)q\left(x\right)=q\left(x\right)q\left(x\right)-q\left(x\right)q(xq(x)q(x)\text{=}q(x)\text{=f}q(x)\text{=} | q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(x\right)-f\left(x\right)\cdot g^{\prime}\left(x\right)}{\left(g\left(x\right)\right)^2}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(x\right)-f\left(x\right)\cdot g^{\prime}\left(x\right)}{\left(g\left(x\right)\right)}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(x\right)-f\left(x\right)\cdot g^{\prime}\left(x\right)}{\left(g\left(x\right)\right)}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(x\right)-f\left(x\right)\cdot g^{\prime}\left(x\right)}{\left(g\left(x\right)\right)}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(x\right)-f\left(x\right)\cdot g^{\prime}\left(x\right)}{\left(g\left(\right)\right)}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(x\right)-f\left(x\right)\cdot g^{\prime}\left(x\right)}{\left(g\right)}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(x\right)-f\left(x\right)\cdot g^{\prime}\left(x\right)}{\left(\placeholder{}\right)}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(x\right)-f\left(x\right)\cdot g^{\prime}\left(x\right)}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(x\right)-f\left(x\right)\cdot g^{\prime}\left(x\right)}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(x\right)-f\left(x\right)\cdot g^{\prime}\left(\right)}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(x\right)-f\left(x\right)\cdot g^{\prime}}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(x\right)-f\left(x\right)\cdot g}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(x\right)-f\left(x\right)\cdot}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(x\right)-f\left(x\right)}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(x\right)-f\left(x\right)}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(x\right)-f\left(x\right)}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(x\right)-f\left(\right)}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(x\right)-f}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(x\right)-}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(x\right)}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(x\right)}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(\right)}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(g\right)}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(g\right)}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g\left(\right)}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot g}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)\cdot}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(x\right)}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f^{\prime}\left(\right)}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f^{\prime}}{\placeholder{}}q^{\prime}\left(x\right)=\frac{f}{\placeholder{}}q^{\prime}\left(x\right)=\frac{\placeholder{}}{\placeholder{}}q^{\prime}\left(x\right)=q^{\prime}\left(x\right)q^{\prime}\left(x\right)q^{\prime}\left(\right)q^{\prime}q |
kettingregel | k\left(x\right)=f\left(g\left(x\right)\right)k\left(x\right)=f\left(g\left(x\right)\right)k\left(x\right)=f\left(g\left(x\right)\right)k\left(x\right)=f\left(g\left(\right)\right)k\left(x\right)=f\left(g\left(c\right)\right)k\left(x\right)=f\left(g\left(\right)\right)k\left(x\right)=f\left(g\right)k\left(x\right)=f\left(\right)k\left(x\right)=f\left(f\right)k\left(x\right)=f\left(\right)k\left(x\right)=fk\left(x\right)=k\left(x\right)k\left(x\right)k\left(\right)k | k^{\prime}\left(x\right)=f^{\prime}\left(g\left(x\right)\right)\cdot g^{\prime}\left(x\right)of\frac{\text{d}k}{\text{d}x}=\frac{\text{d}f}{\text{d}g}\cdot\frac{\text{d}g}{\text{d}x}\frac{\text{d}k}{\text{d}x}=\frac{\text{d}f}{\text{d}g}\cdot\frac{\text{d}g}{x}\frac{\text{d}k}{\text{d}x}=\frac{\text{d}f}{\text{d}g}\cdot\frac{g}{x}\frac{\text{d}k}{\text{d}x}=\frac{\text{d}f}{\text{d}g}\cdot\frac{g}{\placeholder{}}\frac{\text{d}k}{\text{d}x}=\frac{\text{d}f}{\text{d}g}\cdot g\frac{\text{d}k}{\text{d}x}=\frac{\text{d}f}{\text{d}g}\cdot\frac{\text{d}k}{\text{d}x}=\frac{\text{d}f}{\text{d}g}\frac{\text{d}k}{\text{d}x}=\frac{\text{d}f}{g}\frac{\text{d}k}{\text{d}x}=\frac{f}{g}\frac{\text{d}k}{\text{d}x}=\frac{f}{\placeholder{}}\frac{\text{d}k}{\text{d}x}=f\frac{\text{d}k}{\text{d}x}=\frac{\text{d}k}{\text{d}x}=\frac{\text{d}k}{\text{d}x}=\frac{\text{d}k}{\text{d}x}=\frac{\text{d}k}{\text{d}x}=\frac{\text{d}k}{\text{d}x}=\frac{\text{d}k}{\text{d}x}=\frac{\text{d}k}{\text{d}x}=\frac{\text{d}k}{\text{d}x}\frac{\text{d}k}{x}\frac{k}{x}\frac{k}{x}\frac{k}{x}\frac{k}{x}\frac{k}{x}\frac{k}{x}\frac{k}{x}\frac{k}{x}\frac{k}{x}\frac{k}{\placeholder{}}\frac{\placeholder{}}{\placeholder{}}d |
Logaritmen
regel | voorwaarde |
|---|---|
^{g}\log\left(a\right)+\,^{g}\log\left(b\right)=\,^{g}\log\left(ab\right)^{g}\log\left(a\right)+\,^{g}\log\left(\right)=\,^{g}\log\left(ab\right)^{g}\log\left(a\right)+\,^{g}\log\left(a\right)=\,^{g}\log\left(ab\right)^{g}\log\left(a\right)+^{g}\log\left(a\right)=\,^{g}\log\left(ab\right)^{g}\log\left(a\right)+^{g}\log\left(a\right)=\,^{g}\log\left(ab\right)^{g}\log\left(a\right)+^{g}\log\left(a\right)=\,^{g}\log\left(ab\right)^{g}\log\left(a\right)+^{g}\log\left(a\right)=^{g}\log\left(ab\right)^{g}\log\left(a\right)+^{g}\log\left(a\right)=^{g}\log\left(ab\right)^{g}\log\left(a\right)+^{g}\log\left(a\right)=^{g}\log\left(ab\right)^{g}\log\left(a\right)+^{g}\log\left(a\right)=^{g}\log\left(a\right)^{g}\log\left(a\right)+^{g}\log\left(a\right)=^{g}\log\left(a\right)+^{g}\log\left(a\right)^{g}\log\left(a\right)+^{g}\log\left(a\right)^{g}\log\left(\right)^{g}\log\left(d\right)^{g}\left(d\right)^{g}l\left(d\right)^{g}\left(d\right)^{g}\log_{\placeholder{}}\left(d\right)^{g}\log_{\placeholder{}}\left(\right)^{g}\log_{\placeholder{}}^{g}lo^{g}l^{g}^{g}\log_{\placeholder{}}^{g}lo^{g}l^{g}^{g}\log_{}^{g}\log_{\left.\right)}^{g}\log_{\left(\right)}^{g}\log_{\left(a\right)}^{g}\log_{\left(\placeholder{}\right)}^{g}\log_{\placeholder{}}^{g}lo^{g}l^{g}^{9g}^9 | g>0{,}\,g\ne1{,}\,a>0{,}\,b>0g>0{,}\,g\ne1{,}\,a>0{,}\,b>g>0{,}\,g\ne1{,}\,a>0{,}\,bg>0{,}\,g\ne1{,}\,a>0{,}\,g>0{,}\,g\ne1{,}\,a>0{,}g>0{,}\,g\ne1{,}\,a>0{,}g>0{,}\,g\ne1{,}\,a>0{,}g>0{,}\,g\ne1{,}\,a>\frac{0{,}}{}g>0{,}\,g\ne1{,}\,a>\frac{0{,}}{b}g>0{,}\,g\ne1{,}\,a>\frac{0{,}}{\placeholder{}}g>0{,}\,g\ne1{,}\,a>0{,}g>0{,}\,g\ne1{,}\,a>0{,}bg>0{,}\,g\ne1{,}\,a>0{,}g>0{,}\,g\ne1{,}\,a>0g>0{,}\,g\ne1{,}\,a>g>0{,}\,g\ne1{,}\,a>-g>0{,}\,g\ne1{,}\,a>g>0{,}\,g\ne1{,}\,ag>0{,}\,g\ne1{,}\,g>0{,}\,g\ne1{,}g>0{,}\,g\ne1{,}g>0{,}\,g\ne1{,}g>0{,}\,g\ne1g>0{,}\,g\neg>0{,}\,gg>0{,}\,g>0{,}g>0{,}g>0{,}g>0g>g |
^{g}\log\left(a\right)-\,^{g}\log\left(b\right)=\,^{g}\log\left(\frac{a}{b}\right)^{g}\log\left(a\right)-\,^{g}\log\left(b\right)=\,^{g}\log\left(\frac{a}{\placeholder{}}\right)^{g}\log\left(a\right)-\,^{g}\log\left(b\right)=\,^{g}\log\left(a\right)^{g}\log\left(a\right)-\,^{g}\log\left(b\right)=\,^{g}\log\left(ab\right)^{g}\log\left(a\right)\,^{g}\log\left(b\right)=\,^{g}\log\left(ab\right) | g>0{,}\,g\ne1{,}\,a>0{,}\,b>0 |
^{g}\log\left(a^{p}\right)=p\cdot\,^{g}\log\left(a\right)^{g}\log\left(a^{p}\right)=p\cdot\,^{g}\log\left(a\right)=\,^{g}\log\left(ab\right)^{g}\log\left(a^{p}\right)=p\cdot\,^{g}\log\left(\right)=\,^{g}\log\left(ab\right)^{g}\log\left(a^{p}\right)=p\cdot\,^{g}\log\left(b\right)=\,^{g}\log\left(ab\right)^{g}\log\left(a^{p}\right)=p\cdot\,^{g}\log\left(ba\right)=\,^{g}\log\left(ab\right)^{g}\log\left(a^{p}\right)=p\cdot\,^{g}\log\left(b\right)=\,^{g}\log\left(ab\right)^{g}\log\left(a^{p}\right)=p\cdot+\,^{g}\log\left(b\right)=\,^{g}\log\left(ab\right)^{g}\log\left(a^{p}\right)=p\cdot+^{g}\log\left(b\right)=\,^{g}\log\left(ab\right)^{g}\log\left(a^{p}\right)=p\cdot+\,^{g}\log\left(b\right)=\,^{g}\log\left(ab\right)^{g}\log\left(a^{p}\right)=p+\,^{g}\log\left(b\right)=\,^{g}\log\left(ab\right)^{g}\log\left(a^{p}\right)=+\,^{g}\log\left(b\right)=\,^{g}\log\left(ab\right)^{g}\log\left(a^{p}\right)+\,^{g}\log\left(b\right)=\,^{g}\log\left(ab\right) | g>0{,}\,g\ne1{,}\,a>0g>0{,}\,g\ne1{,}\,a>0{,}g>0{,}\,g\ne1{,}\,a>0{,}\,g>0{,}\,g\ne1{,}\,a>0{,}\,bg>0{,}\,g\ne1{,}\,a>0{,}\,b>g>0{,}\,g\ne1{,}\,a>0{,}\,b>0 |
^{g}\log\left(a\right)=\,\frac{^{p}\log\left(a\right)}{^{p}\log\left(g\right)}^{g}\log\left(a\right)=\,\frac{^{p}\log\left(a\right)}{^{p}p\log\left(g\right)}^{g}\log\left(a\right)=\,\frac{^{p}\log\left(a\right)}{p\log\left(g\right)}^{g}\log\left(a\right)=\,\frac{^{p}\log\left(a\right)}{p\log\left(\right)}^{g}\log\left(a\right)=\,\frac{^{p}\log\left(a\right)}{p\log\left(a\right)}^{g}\log\left(a\right)=\,\frac{^{p}\log\left(a\right)}{\placeholder{}}^{g}\log\left(a\right)=\,\frac{\left(^{p}\log\left(a\right)\right.}{\placeholder{}}^{g}\log\left(a\right)=\,\frac{\left(^{p}\log\left(a\right)\right)}{\placeholder{}}^{g}\log\left(a\right)=\,\frac{\left(^{p}\log\left(\right)\right)}{\placeholder{}}^{g}\log\left(a\right)=\,\frac{\left(^{p}\log\left(b\right)\right)}{\placeholder{}}^{g}\log\left(a\right)=\,\frac{\left(^{pg}\log\left(b\right)\right)}{\placeholder{}}^{g}\log\left(a\right)=\,\frac{\left(^{g}\log\left(b\right)\right)}{\placeholder{}}^{g}\log\left(a\right)=\,\left(^{g}\log\left(b\right)\right)^{g}\log\left(a\right)=\,\left(^{g}\log\left(b\right)\right.^{g}\log\left(a\right)=\,\left(^{g}\log\left(b\right)=\right.^{g}\log\left(a\right)=\,\left(^{g}\log\left(b\right)=\,\right.^{g}\log\left(a\right)=\,\left(^{g}\log\left(b\right)=\,^{}\right.^{g}\log\left(a\right)=\,\left(^{g}\log\left(b\right)=\,^{g}\right.^{g}\log\left(a\right)=\,\left(^{g}\log\left(b\right)=\,^{g}\log\right.^{g}\log\left(a\right)=\,\left(^{g}\log\left(b\right)=\,^{g}\log\left(\right.\right.^{g}\log\left(a\right)=\,\left(^{g}\log\left(b\right)=\,^{g}\log\left(a\right.\right.^{g}\log\left(a\right)=\,\left(^{g}\log\left(b\right)=\,^{g}\log\left(ab\right.\right.^{g}\log\left(a\right)=\,\left(^{g}\log\left(b\right)=\,^{g}\log\left(ab\right)\right.^{g}\log\left(a\right)=\,\left(^{g}\log\left(b\right)=\,^{g}\log\left(ab\right)\right)^{g}\log\left(a\right)=\,^{g}\log\left(b\right)=\,^{g}\log\left(ab\right)^{g}\log\left(a\right)\,^{g}\log\left(b\right)=\,^{g}\log\left(ab\right)\frac{^{g}\log\left(a\right)}{\placeholder{}}\,^{g}\log\left(b\right)=\,^{g}\log\left(ab\right)^{g}\log\left(a\right)\,^{g}\log\left(b\right)=\,^{g}\log\left(ab\right)^{g}\log\left(a\right)+\,^{g}\log\left(b\right)=\,^{g}\log\left(ab\right) | g>0{,}\,g\ne1{,}\,a>0{,}\,p>0{,}\,p\ne1g>0{,}\,g\ne1{,}\,a>0{,}\,p>0{,}\,p\neg>0{,}\,g\ne1{,}\,a>0{,}\,p>0{,}\,pg>0{,}\,g\ne1{,}\,a>0{,}\,p>0{,}\,g>0{,}\,g\ne1{,}\,a>0{,}\,p>0{,}g>0{,}\,g\ne1{,}\,a>0{,}\,p>0{,}g>0{,}\,g\ne1{,}\,a>0{,}\,p>0{,}g>0{,}\,g\ne1{,}\,a>0{,}\,p>0g>0{,}\,g\ne1{,}\,a>0{,}\,>0g>0{,}\,g\ne1{,}\,a>0{,}\,b>0 |
