Question

Find dy/dx for y=cos inverse of [(1-x^{2})/(1+x^{2})] ?

Answer 1

plz see the upload hope it helps

Answer 2

$y = {cos}^{ - 1} ( \frac{1 - {x}^{2} }{1 + {x}^{2} } ) \\ \\ put \: \: x = tan \theta \\ \\ y = {cos}^{ - 1} ( \frac{1 - {tan}^{2} \theta }{1 + {tan}^{2} \theta } ) \\ \\ y = {cos}^{ - 1} (cos2 \theta) \\ \\ y = 2\theta \\ \\ y = 2{tan}^{ - 1} x \\ \\ \frac{dy}{dx} = \frac{2}{1 + {x}^{2} }$