# How do you differentiate f(x)=cos(tanx) using the chain rule?

Oct 29, 2015

$\frac{d}{\mathrm{dx}} \left(\cos u\right) = - \sin u \frac{d}{\mathrm{dx}} \left(u\right)$
$f ' \left(x\right) = - \sin \left(\tan x\right) \frac{d}{\mathrm{dx}} \left(\tan x\right)$
$= - \sin \left(\tan x\right) {\sec}^{2} x$