Question

The derivative of tan x with respect to x is ? 1-tan x^2

Answer 1

`color(brown)((d / (dx)) tan x = sec ^2 x = 1 + tan^2 x`

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`

`(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 ^2 x = sec ^2 x = 1 + tan^2 x`