Question

Find the derivative of `(x+cosx)/tanx`?

Answer 1

Derivative is `(tanx-sinxtanx+xsec^2x+secx)/tan^2x`

Explanation:

We use quotient rule, which says that derivative of `(f(x))/(g(x))` is

`(g(x)f'(x)-f(x)g'(x))/[g(x)]^2`

Hence derivative of `(x+cosx)/tanx` is

`(tanx(1-sinx)-(x+cosx)xx(-sec^2x))/tan^2x`

= `(tanx-sinxtanx+xsec^2x+secx)/tan^2x`