Derivatives of Trig Functions

Question

Find 

Options:

1. e^3lnx
2. 
3. 3e^3lnx
4. 3x²

Answer 1

Use the chain rule:

If you have something of the form f(g(x)), then f' = f'(g(x)) * g'(x)

Example:

Suppose you have f(x) = (sin(x))²

The derivative is 2*sin(x) * cos(x)

If you have f(x) = e^sin(x) , then

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