#math/calculus The six basic trigonometric derivatives are: | $f(x)$ | $f'(x)$ | |---|---| | $\sin x$ | $\cos x$ | | $\cos x$ | $-\sin x$ | | $\tan x$ | $\sec^{2}x$ | | $\cot x$ | $-\csc^{2}x$ | | $\sec x$ | $\sec x\tan x$ | | $\csc x$ | $-\csc x\cot x$ | These formulas hold wherever the original function is defined. For example, the quotient rule and $\tan x=\sin x/\cos x$ give $(\tan x)'=\frac{\cos^{2}x+\sin^{2}x}{\cos^{2}x}=\sec^{2}x.$ For a differentiable inner function $u(x)$, multiply the corresponding derivative by $u'(x)$; for example, $(\tan u)'=\sec^{2}(u)u',\qquad (\sec u)'=\sec(u)\tan(u)u'.$