The product rule is used to find the derivative of
Look at this and figure out how you differentiate that identity.
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?