Question

if f(x)=(1+tan x)/(1-tan x) then f'(x)=​

Answer 1

Step-by-step explanation:

Given,

$f(x) = \frac{(1 + \tan(x) )}{(1 - \tan(x)) }$

$= > f(x) = \frac{ \tan( \frac{\pi}{4} ) + \tan(x) }{1 - \tan( \frac{\pi}{4} ). \tan(x) }$

$= > f(x) = \tan( \frac{\pi}{4} + x)$

Now,

$\frac{d(f(x))}{dx} = \frac{1}{1 + ( \frac{\pi}{4} + x)^{2} }$

$= \frac{1}{1 + \frac{\pi^{2} }{16} + {x}^{2} + \frac{\pi.x}{2} }$

$= \frac{16}{16 + {\pi}^{2} + 16 {x}^{2} + 8\pi.x }$