# Math Help - Trig Derivitive Question

1. ## Trig Derivitive Question

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?

2. The product rule is used to find the derivative of $x \; sin(x)$

Look at this and figure out how you differentiate that identity.

3. Product rule (u x v)' = (u' x v) + (u x v')

4. Originally Posted by tintin2006
Product rule (u x v)' = (u' x v) + (u x v')
Man I feel so silly now since the reason was so obvious. Thanks.