Not sure if this is a Calc or a trig question. But I wanted to take the derivative of this function:

$\displaystyle y = -csc\,x - sin\,x$

Through simple steps I got:

$\displaystyle -\frac{d}{dx}(csc\,x)\,-\,\frac{d}{dx}sin\,x$

$\displaystyle csc\,x\,cot\,x\,-\,cos\,x$

However the answer in the book is...

$\displaystyle cos\,x\,cot^2\,x$

So presumably my calculus is wrong, or I didn't simplify enough. I have tried various transformations but never quite end up with that. Can anybody show me how to simplify to that?