This is part of an indeterminate form question in my textbook.

lim(x -> 0) ((1/x) - (1/sin x)) = lim (x->0) (sinx - x)/(x sinx) = lim (x->0) (cosx -1) / (sinx + x cosx).

How did the derivitve of (x sinx) become (sinx + x cosx)? Am I forgetting an identitiy that is applied here?