Lukion taulukot/Derivaattafunktioita

Derivaattafunktioita

$f(x)$	$f^{\prime }(x)$
$x^n(n\in ℝ)$	$n{x}^{n-1}$
$(f(x){)}^n$	$n(f(x){)}^{n-1}\cdot f^{\prime }(x)$
$\frac{1}{x}$	$-\frac{1}{x^2}$
$\sqrt{x}$	$\frac{1}{2\sqrt{x}}$
$\sin x$	$\cos x$
$\cos x$	$-\sin x$
$\tan x$	$1+{\tan }^{2}x=\frac{1}{{\cos }^{2}x}$
$\cot x$	$\begin{array}{c}-(1+{\cot }^{2}x)=\\ -\frac{1}{{\sin }^{2}x}\end{array}$
$e^x$	$e^x$
$a^x(a>0)$	$a^x\ln a$
$\ln x(x>0)$	$\frac{1}{x}$
${\log }_{a}x(a,x>0,a\ne 1)$	$\frac{1}{x\ln a}$
$\arcsin x$	$\frac{1}{\sqrt{1-x^2}}$
$\arccos x$	$-\frac{1}{\sqrt{1-x^2}}$
$\arctan x$	$\frac{1}{1+x^2}$
$\mathrm{arccot}x$	$-\frac{1}{1+x^2}$