This is a pretty simple one I guess but I'm not understanding whats happening here two part question:

First simply finding d/dx(4^x)?

The ti-89 says 2*ln(2)*4^x and I'm not getting the mechanics of it.

This is all part of a larger problem which is:

Find f'(x): (4^x*x^(1/3))/tanx

Do I use the product rule seperately to get the deriv of the numerator and then do the quotient rule for the new numerator/tan(x)?