If `x^m y^n=(x+y)^(m+n),` prove that `(dy)/(dx)=y/x` .

Explanation

To prove that \(\frac{dy}{dx} = \frac{y}{x}\) given that \(x^m y^n = (x+y)^{m+n}\), we will follow these steps:

### Step 1: Take the logarithm of both sides
We start with the equation:
\[ x^m y^n = (x+y)^{m+n} \]
Taking the logarithm of both sides, we get:
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