Question

How do you differentiate `f(x)=cot(x)cos(x)` using the product rule?

Answer 1

This is more a pointer in the correct direction:

Explanation:

Once you know that `d/dx(cot(x)) = -1-cot^2(x)`

and you combine it with `d/dx (uv) = v(du)/dx + u(dv)/dx`

You are off to a flying start. Just substitute and play until you find a solution:

As a check I put it into Maple which gave: `(-1 -cot^2{x})cos(x) -cot(x)sin(x)`

Maple outputs are sometimes a little 'Maple'ish' so need to be translated.

remember that `cot(x) = 1/(tan(x)) = (cos(x))/(sin(x))`
so you may be able to use:

`-cos(x)-(cos^3(x))/( sin^2(x)) - (cos(x)sin(x))/(sin(x))`