Lukion taulukot/Derivaattafunktioita

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Derivaattafunktioita

$f(x)$	$f'(x)$
$x^{n}(n\in \mathbb {R} )$	$nx^{n-1}$
$(f(x))^{n}$	$n(f(x))^{n-1}\cdot f'(x)$
${\frac {1}{x}}$	$-{\frac {1}{x^{2}}}$
${\sqrt {x}}$	${\frac {1}{2{\sqrt {x}}}}$
$\sin x$	$\cos x$
$\cos x$	$-\sin x$
$\tan x$	$1+\tan ^{2}x={\frac {1}{\cos ^{2}x}}$
$\cot x$	${\begin{aligned}-(1+\cot ^{2}x)=\\-{\frac {1}{\sin ^{2}x}}\end{aligned}}$
$e^{x}$	$e^{x}$
$a^{x}(a>0)$	$a^{x}\ln a$
$\ln x(x>0)$	${\frac {1}{x}}$
$\log _{a}x(a,x>0,a\neq 1)$	${\frac {1}{x\ln a}}$
$\arcsin x$	${\frac {1}{\sqrt {1-x^{2}}}}$
$\arccos x$	$-{\frac {1}{\sqrt {1-x^{2}}}}$
$\arctan x$	${\frac {1}{1+x^{2}}}$
$\operatorname {arccot} x$	$-{\frac {1}{1+x^{2}}}$