Find the derivative of d/dx (e^sin3x)?

Answer 1

This function is of the type f(x)=e^g(x) where g(x)=sin(3x).

The derivative is therefore f'(x)=e^g(x)g'(x) which in our cases is f'(x)=e^sin(3x) cos(3x)*3 where we have used the chain rule to evaluate the derivative of sin(3x). In fact, the derivative of sin(3x) is equal to cos(3x)*3.

Best,

Davide