How do I solve this math question?

Question

asked Mar 26, 2022 50.8k views

1 Answer

Jmblackmer · Answer 1 · 2022-03-30T21:36:11+0000

Answer:

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

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.

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