# What is the derivative of f(theta)=e^(sin2theta) ?

Aug 3, 2014

$f ' \left(\theta\right) = 2 \cos \left(2 \theta\right) {e}^{\sin} \left(2 \theta\right)$

Explanation,

let's we have $u \left(\theta\right) = {e}^{g} \left(f \left(\theta\right)\right)$

then, using Chain Rule ,

$u ' \left(\theta\right) = {e}^{g} \left(f \left(\theta\right)\right) \left(g ' f \left(\theta\right)\right) f ' \left(\theta\right)$

Similarly differentiating the given function with respect to $\theta$,

$f \left(\theta\right) = {e}^{\sin} \left(2 \theta\right)$

$f ' \left(\theta\right) = {e}^{\sin} \left(2 \theta\right) \left(\cos \left(2 \theta\right)\right) \left(2\right)$

$f ' \left(\theta\right) = 2 \cos \left(2 \theta\right) {e}^{\sin} \left(2 \theta\right)$