Explanation

(b)
Given, $x^{m}y^{n} = (x + y)^{m + n}$
$m\log{x + n\log{y = (m + n)\log(x + y)}}$
$\frac{m}{x} + \frac{n}{y}\frac{dy}{dx} = \frac{(m + n)}{(x + y)}\left\lbrack 1 + \frac{dy}{dx} \right\rbrack$
$\Rightarrow \ \frac{dy}{dx}\left\lbrack \frac{n}{y} - \frac{(m + n)}{(x + y)} \right\rbrack = \frac{m + n}{x + y} - \frac{m}{x}$
$\Rightarrow \ \frac{dy}{dx} = \frac{y}{x}$
$\Rightarrow \ \left( \frac{dy}{dx} \right)_{x = 1,y = 2} = 2$