Answer:
[tex] - \frac{sec^{2}x }{2 \tan (\frac{3}{2} ) x} [/tex]
Step-by-step explanation:
use chain rule on
[tex] \frac{d}{dx} \frac{1}{ \sqrt{ \tan\: (x)} } [/tex]
Let u = tan x.
Use power rule
[tex] \frac{d}{du} {u}^{n} = nu ^{n - 1} [/tex]
[tex] - \frac{1}{2 \tan( \frac{3}{2}x ) } ( \frac{d}{dx} \tan \: (x) )[/tex]
Use Trigonometric Differentiation: the derivative of tan x is sec² x.
[tex] - \frac{ \sec^{2} x}{2 \tan( \frac{3}{2} ) x} [/tex]
