Question

If f (x) = sin(cos(tan x)). Then find f'(x)​

Answer 1

Answer:

The answer is $-\cos(\cos(\tan x)) (\sin(\tan x)) \sec^2x$

Step-by-step explanation:

Given  $f(x)=\sin(\cos(\tan x))$

Using chain rule of differentiation

$f'(x)=\frac{d(\sin(\cos (\tan x)))}{d(\cos(\tan x))}\times \frac{{d(\cos(\tan x))}}{d(\tan x)}\times \frac{d(\tan x)}{dx}$

         $=\cos(\cos(\tan x))\times (-\sin(\tan x))\times \sec^2x\\=-\cos(\cos(\tan x)) (\sin(\tan x)) \sec^2x$