Mathematics - Differentiation Question with Solution | TestHub

$x^m\cdot y^n=(x+y{)}^{m+n}\Rightarrow m\ln x+n\ln y=(m+n)\ln (x+y)$ $\therefore \frac{m}{x}+\frac{n}{y}\frac{dy}{dx}=\frac{m+n}{x+y}\left(1+\frac{dy}{dx}\right)\Rightarrow \left(\frac{m}{x}-\frac{m+n}{x+y}\right)=\left(\frac{m+n}{x+y}-\frac{n}{y}\right)\frac{dy}{dx}$ $\frac{my-nx}{x(x+y)}=\left(\frac{my-nx}{y(x+y)}\right)\frac{dy}{dx}\Rightarrow \frac{dy}{dx}=\frac{y}{x}$