# How do you differentiate f(x)=sece^(4x) using the chain rule.?

Feb 12, 2016

$f ' \left(x\right) = 4 {e}^{4 x} \sec \left({e}^{4 x}\right) \cdot \tan \left({e}^{4 x}\right)$
By the chain rule, if $y = f \left(u\right) \mathmr{and} u = f \left(x\right)$. then
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\mathrm{dy}}{\mathrm{du}} \cdot \frac{\mathrm{du}}{\mathrm{dx}}$
$\therefore \frac{d}{\mathrm{dx}} \left[\sec \left({e}^{4 x}\right)\right] = \sec \left({e}^{4 x}\right) \cdot \tan \left({e}^{4 x}\right) \cdot {e}^{4 x} \cdot 4$