Question

How do you differentiate `f(x)=sinx-1/(xcosx)` using the sum rule?

Answer 1

`D_x f(x) = cos x + (cos x + x sin x)/(x^2 cos^2 x)`

Explanation:

`D_x f = cos x - D_x 1/u` where `u = x cos x`

`D_x f = cos x + 1/u^2 D_x (x cos x)`

`D_x f = cos x + 1/u^2 (1 cos x + x sin x)`