Question

What is the derivative of `e^sin(x^2)`?

Answer 1

`2xe^(sin(x^2))cos(x^2)`

Explanation:

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

`f(x) = e^(g(x))` Where `g(x)= sin(x^2)`

`f'(x) = d/dx e^(g(x)) = e^(g(x))* g'(x)` By the Chain Rule

`f'(x) = e^(sin(x^2)) * cos (x^2) * d/dx x^2` By the Chain Rule again

`f'(x) = e^(sin(x^2)) * cos (x^2) * 2x`

`f'(x) = 2xe^(sin(x^2))cos(x^2)`