Question

How do you differentiate `f(x)=cot(x/2)sin(x/2)`?

Answer 1

Use `cot(x/2) = cos(x/2)/sin(x/2)` to simplify first.

Explanation:

After simplifying, we have `f(x) = cos(x/2)` `" "` (`x != 2pin`, for `n` an integer.)

Use the chain rule to get

`f'(x) = -1/2sin(x/2)` `" "` (`x != 2pin`, for `n` an integer.)