Derivasjonsreglar

Definisjon

$f\text{'}\left(x\right)=\underset{∆x\to 0}{\lim }\frac{f(x+∆x)-f\left(x\right)}{∆x}$

Konstant funksjon

$f\left(x\right)=k$

$f\text{'}\left(x\right)=0$

Potensfunksjonar

$f\left(x\right)=x^r$

$f\text{'}\left(x\right)=r·x^{r-1}$

Funksjon multiplisert
med konstant

$f\left(x\right)=k·g\left(x\right)$

$f\text{'}\left(x\right)=k·g\text{'}\left(x\right)$

Summar og differansar

$f\left(x\right)=g\left(x\right)\pm h\left(x\right)$

$f\text{'}\left(x\right)=g\text{'}\left(x\right)\pm h\text{'}\left(x\right)$

Produkt

$f\left(x\right)=u\left(x\right)·v\left(x\right)$

$f\text{'}\left(x\right)=u\text{'}\left(x\right)·v\left(x\right)+u\left(x\right)·v\text{'}\left(x\right)$

Brøkfunksjonar

$f\left(x\right)=\frac{u\left(x\right)}{v\left(x\right)}$

$f\text{'}\left(x\right)=\frac{u\text{'}\left(x\right)·v\left(x\right)-u\left(x\right)·v\text{'}\left(x\right)}{{\left(v\left(x\right)\right)}^2}$

Eksponentialfunksjonar

$f\left(x\right)=e^x$

$f\text{'}\left(x\right)=e^x$

$f\left(x\right)=a^x$

$f\text{'}\left(x\right)=a^x·\ln a$

Logaritmefunksjonar

$f\left(x\right)=\ln x$

$f\text{'}\left(x\right)=\frac{1}{x}$