Help me with this math problem? (Calculus)?

Make sure that the answer in the book isn't actually the same as your answer, but in a different form due to some trig identity. Just plug some fixed value in both your answer and theirs to see if you get the same thing or not. I don't have the time to check your work right now (it's been a while since I did derivatives of this sort and sadly, I'd have to look up how to do it now) but I remember back in the day when I was taking calc and doing this stuff, this would happen to me all the time. My answer would be correct but in a different form than the book. Check it to see if that's it.