Table of fundamental derivatives

The derivatives of the elementary functions must be known by heart: they are the “building blocks” from which, using the rules of differentiation, one constructs the derivative of any expression.

In brief — Derivatives of the elementary functions

$f(x)$	$f'(x)$	$f(x)$	$f'(x)$
$k$	$0$	$\sin x$	$\cos x$
$x^n$	$nx^{n-1}$	$\cos x$	$-\sin x$
$e^x$	$e^x$	$\tan x$	$1/\cos^2 x$
$a^x$	$a^x\ln a$	$\arcsin x$	$1/\sqrt{1-x^2}$
$\ln x$	$1/x$	$\arccos x$	$-1/\sqrt{1-x^2}$
$\log_a x$	$1/(x\ln a)$	$\arctan x$	$1/(1+x^2)$

Links

Topics: Derivatives
Concepts: Derivative · Fundamental derivatives
Skills: Differentiating · Using formulae