Question

How do you differentiate `f(x)=sin(e^(x^2-2))` using the chain rule?

Answer 1

`f'(x)=2xe^(x^2-2)cos(e^(x^2-2))`

Explanation:

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

Use the chain rule to differentiate (derivative of the outside times derivative of the inside):

`f'(x)=cos(e^(x^2-2))(2xe^(x^2-2))`

`f'(x)=2xe^(x^2-2)cos(e^(x^2-2))`