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: (A)

$\frac{x+y}{xy}$

$x^m{y}^n=(x+y{)}^{m+n}$
$\log x^m{y}^n=\log (x+y{)}^{m+n}$
$\log x^m+\log y^n=(m+n)\log (x+y)$
$m\log x+n\log y=(m+n)\log (x+y)$
different wrtx
$m\frac{1}{x}+\frac{n}{y}.\frac{dy}{dx}=\frac{m+n}{x+y}(1+\frac{dy}{dx})$
$(\frac{n}{y}-\frac{m+n}{x+y}).\frac{dy}{dx}=\frac{m+n}{x+y}-\frac{m}{x}$
$\frac{nx+ny-my-ny}{y(x+y)}.\frac{dy}{dx}=\frac{mx+nc-mx-my}{x(x+y)}$
$\frac{(nx-my)}{y}\frac{dy}{dx}=\frac{(nx-my)}{x}$
$\frac{dy}{dx}=\frac{y}{x}$