Question

If $x^m{y}^n=(x+y{)}^{m+n}$ , then $\frac{dy}{dx}$ is

• A. $\frac{x+y}{xy}$
• B. $xy$
• C. $\frac{x}{y}$
• D. $\frac{y}{x}$

Answer 1

Answer: (D)

Given, $x^m{y}^n=(x+y{)}^{m+n}$
Taking log on both sides, we get $m\log x+n\log y=(m+n)\log (x+y)$
On differentiating wrt $x$, we get,
$\frac{dy}{dx}=\frac{y}{x}$