Question

How do you differentiate `f(x)=cotx(cscx)`?

Answer 1

`- csc^(3)(x) - csc(x) cot^(2)(x)`

Explanation:

We have: `f(x) = cot(x) csc(x)`

This function can be differentiated using the "product rule":

`=> f'(x) = (d) / (dx) (cot(x)) cdot csc(x) + (d) / (dx) (csc(x)) cdot cot(x)`

`=> f'(x) = - csc^(2)(x) cdot csc(x) + (- csc(x) cot(x)) cdot cot(x)`

`=> f'(x) = - csc^(3)(x) - csc(x) cot^(2)(x)`