Question

find the derivative of f given by f( x) =sin -x assuming it exists​

Answer 1

ANSWER:-

$\sf\red{Let\:y={tan}^{-1}x. Then\: x = tan\:y}$

$\sf\blue{differentiating \: both \: sides \: w.r.t.x, \: we \: get}$

$\sf\red{1 = {sec}^{2} y \frac{dy}{dx}}$

$\sf\green{which\:implies\:that}$

$\sf\red{ \frac{dy}{dx} = \frac{1}{ {sec}^{2}y } = \frac{1}{1 + {tan}^{2} y} = \frac{1}{1 + {(tan( {tan}^{ - 1} x))}^{2}} = \frac{1}{1 + {x}^{2} } }$