Question

Find the derivative ​

Answer 1

Derivate of the given function is $- \frac{2}{(x + \frac{1}{x}) }$

Answer 2

Answer:

$\boxed{ \purple{\bold{- \frac{ 2}{1 + {x}^{2} } }}}$

◆In this question , first solve the Inverse Trigonometry,

by Let

$x = tan \theta \\ or \: \\ \theta = {tan}^{ - 1} x$

●After solving , we get the value

=

$\boxed{- 2 {tan}^{ - 1} x}$

◆ And at last differentiate w.r.t X

Formula used :

$\star\boxed{ \bold{ \green{cos \: 2 \theta = \frac{1 - {tan}^{2} \theta }{1 + {tan}^{2} \theta } }}}$

$\star \boxed{ \red{\bold{ {cos}^{ - 1} (cosx) = x}}}$

$\star \: \boxed{ \orange{\bold{ \frac{d}{dx} ( {tan}^{ - 1} x) = \frac{1}{1 + {x}^{2} } }}}$

Solution refer to the attachment