Question

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

Answer 1

`f'(theta)=2cos(2theta)e^sin(2theta)`

Explanation,

let's we have `u(theta)=e^g(f(theta))`

then, using Chain Rule ,

`u'(theta)=e^g(f(theta))(g'f(theta))f'(theta)`

Similarly differentiating the given function with respect to `theta`,

`f(theta)=e^sin(2theta)`

`f'(theta)=e^sin(2theta)(cos(2theta))(2)`

`f'(theta)=2cos(2theta)e^sin(2theta)`