3.11 Standard Derivatives

In the following table of derivatives, $a$ is a constant.

$f(x)$    $f^{\prime}(x)$

$x^{n}$    $nx^{n-1}$ for all $n\in{\mathbb{N}}$ and $x\in{\mathbb{R}}$;

$x^{a}$    $ax^{a-1}$ for all $a\in{\mathbb{R}}$ and $x>0$;

$e^{ax}$     $ae^{ax};$

$\log|ax|$    $1/x$ for all $x\neq 0$;

$\sin ax$    $a\cos ax;$

$\cos ax$    $-a\sin ax;$

$\tan ax$    $a\sec^{2}ax$ for all $x$ such that $\cos ax\neq 0.$