Question

If $x^m y^n=2(x+y)^{m+n}$, the value of $\frac{d y}{d x}$ is

(A) $x+y$

(B) $\frac{x}{y}$

(C) $\frac{y}{x}$

(D) $x-y$

Answer 1

$\text { } x^m y^n=2(x+y)^{m+n} $

$\Rightarrow \quad m \log x+n \log y=\log 2+(m+n) \log (x+y) $

$\Rightarrow \quad \frac{m}{x}+\frac{n}{y} \frac{d y}{d x}=\frac{m+n}{x+y}\left[1+\frac{d y}{d x}\right] $

$\Rightarrow \quad \frac{d y}{d x}\left(\frac{m+n}{x+y}-\frac{n}{y}\right)=\frac{m}{x}-\frac{m+n}{x+y} $

$\Rightarrow \quad \frac{d y}{d x}=\frac{y}{x} $

So, The correct option will be (C).