Answer
$(cosx)' = -sinx$
Work Step by Step
$f'(x)$ = $\lim\limits_{h \to 0} \frac{cos(x+h)-cosx}{h}$
= $\lim\limits_{h \to 0} \frac{(cosx)(cosh)-(sinx)(sinh)-cosx}{h}$
= $\lim\limits_{h \to 0}cosx\frac{[cosh-1]}{h}-sinx[\frac{sinh}{h}]$
= $cosx(0)-sinx(1)$
= $-sinx$
