Question

cos ^-1 ( x/1+x) differentiate w.r.t.x ​

Answer 1

Step-by-step explanation:

Let

$y = \cos^{ - 1} ( \frac{x}{1 + x} )$

Differentiating both sides we get,

$\frac{dy}{dx} = \frac{ - 1}{ \sqrt{1 - { (\frac{x}{1 + x}) }^{2} } } . \frac{d}{dx} ( \frac{x}{1 + x} )$

$= > \frac{dy}{dx} = - \frac{ {(1 + x)}^{2} }{ \sqrt{( {1 + x)}^{2} - {x}^{2} } } . \frac{1(1 + x) - x(1)}{(1 + x)^{2} }$

$= > \frac{dy}{dx} = - \frac{1}{ \sqrt{1 + {x}^{2} + 2x - {x}^{2} } }$

$= > \frac{dy}{dx} = \frac{ - 1}{ \sqrt{2x + 1}}$