Question

How do you differentiate `f(x)=cos(xe^(x) )` using the chain rule?

Answer 1

`f'(x)=-( 1 + x ) e^x sin (xe^x)`

Explanation:

Using product rule #(xe^x)' =x(e^x)'+e^x(x)' =xe^x+e^x =( 1 + x )e^x#.

Using chain rule, `(cos(xe(x))'=-sin(xe^x) (xe^x)'=- sin (xe^x)( 1 + x ) e^x`