Question

The derivative of tan x with respect to x is ?

Answer 1

`sec^2x`

Explanation:

`(d/(dx))tan x = (d/(dx)) (sin x / cos x)`

It is in the form `u / v` and the derivative is

`(v du - u dv) / v^2` where `u = sin x, v = cos x`

`(d / (dx)) (sin x / cos x) = cos x * cos x - (sin x * (-sin x)) / cos^2 x`

`=> (cos^2 x + sin ^2 x) / cos^2 x = 1/ cos ^2x = sec^2 x` as `cos^2x + sin^2x = 1`