Question

How do I solve this math question?​

Answer 1

`- (sec^(2)x )/(2 \tan ((3)/(2) ) x)`

Explanation:

use chain rule on

`(d)/(dx) (1)/( √( \tan\: (x)) )`

Let u = tan x.

Use power rule

`(d)/(du) {u}^(n) = nu ^(n - 1)`

`- (1)/(2 \tan( (3)/(2)x ) ) ( (d)/(dx) \tan \: (x) )`

Use Trigonometric Differentiation: the derivative of tan x is sec² x.

`- ( \sec^(2) x)/(2 \tan( (3)/(2) ) x)`