If $\sqrt{x} \sqrt[3]{y} = (x + y)^n$ and $x\frac{dy}{dx} - y = 0$, then $n =$
Show Hint
Memorize this highly useful shortcut result for competitive exams: If $x^m \cdot y^n = (x+y)^{m+n}$, then it is guaranteed that $\frac{dy}{dx} = \frac{y}{x}$. Recognizing this pattern instantly solves the problem without any differentiation.