Question

How do you differentiate `f(x)=csc5x * cot3x` using the product rule?

Answer 1

`f'(x) = -3csc5xcsc^2 3x -5csc5xcot5xcot3x`

Explanation:

Product rule:

`(uv)' = vu' +uv'`

Let `u=cot3xrArr u' = -3csc^2 3x`

And `v=csc5x rArr v'= -5csc5xcot5x`

Then `(csc5x*cot3x)' = -3csc^2 3xcsc5x - 5csc5xcot5xcot3x`