Explanation

(b)
$\because\frac{x^{2} - y^{2}}{x^{2} + y^{2}} = \sec^{- 1}\left( e^{a} \right)$
On differentiating w.r.t. $x$, we get
$\frac{\left( x^{2} + y^{2} \right)\left( 2x - 2y\frac{dy}{dx} \right) - (x^{2} - y^{2})\left( 2x + 2y\frac{dy}{dx} \right)}{\left( x^{2} + y^{2} \right)^{2}} = 0$
$\Rightarrow x\left( x^{2} + y^{2} \right) - y(x^{2} + y^{2})\frac{dy}{dx}$
$= \left( x^{2} - y^{2} \right)x + y(x^{2} - y^{2})\frac{dy}{dx}$
$\Rightarrow \left( x^{2}y - y^{3} + x^{2}y + y^{3} \right)\frac{dy}{dx} = (x^{3} + xy^{2} - x^{3} + xy^{2})$
$\Rightarrow \frac{dy}{dx} = \frac{2xy^{2}}{2x^{2}y} = \frac{y}{x}$