Question

What is the final answer of this ?

Answer 1

$y = e^{\sqrt{\frac{1-x}{1+x} } }$

$logy = \sqrt{\frac{1-x}{1+x} }$

$(logy)^2 = \frac{1-x}{1+x}$

Differentiating with respect to x

$2logy*\frac{1}{y}*\frac{dy}{dx} = \frac{-(1+x) - (1-x)}{(1+x)^2}$

$2logy*\frac{1}{y}*\frac{dy}{dx} = \frac{-2}{(1+x)^2}$

$\frac{dy}{dx} = \frac{-y}{logy(1+x)^2}$

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

$\large\black\boxed{\frac{dy}{dx} = \frac{-e^{\sqrt{\frac{1-x}{1+x} }} }{(1+x)\sqrt{1-x^2 }}}$