Question

$f\left(x\right)=\sec x-\cos x,xϵ(0,\pi /2)$

find f'(x)

Answer 1

Given that,

$f\left(x\right)=\sec x-\cos x(0,\frac{\pi }{2})$

Differentiate bathes sides with respect to $x$,

$f^{{}^{\prime }}\left(x\right)=\sec x.\tan x-(-\sin x)$

$=\sec x.\tan x+\sin x$

Hence this is the answer.