The derivative of a constant raised to a function = the same constant raised to the same function times the natural log of the base times the derivative of the function which is in the exponent.

Edit: I think your answer is okay too, I don't see any reason you couldn't split that up into which would give you the answer that you got. To simplify your answer, you would just end up adding the back into the which would be the same as what is up top.