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

1 Answer
Sep 21, 2016

- csc^(3)(x) - csc(x) cot^(2)(x)csc3(x)csc(x)cot2(x)

Explanation:

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