If `x^(a)cdoty^(b)=(x+y)^(a+b)` then prove that `(dy)/(dx)=y/x`

Explanation

To prove that \(\frac{dy}{dx} = \frac{y}{x}\) given the equation \(x^a \cdot y^b = (x + y)^{a + b}\), we will follow these steps:

### Step 1: Take the logarithm of both sides
We start with the equation:
\[ x^a \cdot y^b = (x + y)^{a + b} \]
Taking the logarithm of both sides:
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