Question

How do you differentiate `f(x)=x/cotx` using the quotient rule?

Answer 1

`f'(x)=(xcsc^2x+cotx)/cot^2x`

Explanation:

According to the Quotient Rule:

`f'(x)=(cotxd/dx[x]-xd/dx[cotx])/cot^2x`

`f'(x)=(cotx(1)-x(-csc^2x))/cot^2x`

`f'(x)=(xcsc^2x+cotx)/cot^2x`