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

Dec 3, 2015

$f ' \left(x\right) = 4 {e}^{4 x} \cos \left({e}^{4 x}\right)$

#### Explanation:

f'(x)=color(red)(cos(e^(4x))color(blue)(d/dx[e^(4x)]

color(blue)(d/dx[e^(4x)])=e^(4x)d/dx[4x]=color(blue)(4e^(4x)

f'(x)=color(blue)(4e^(4x))color(red)(cos(e^(4x))

Notice that the chain rule actually occurred twice.