`"If "log(x^(2)+y^(2))=2tan^(-1)""((y)/(x))," show that "(dy)/(dx)=(x+y)/(x-y)`

Explanation

To solve the problem, we need to differentiate the given equation \( \log(x^2 + y^2) = 2 \tan^{-1}\left(\frac{y}{x}\right) \) with respect to \( x \) and show that \( \frac{dy}{dx} = \frac{x+y}{x-y} \).

### Step-by-step Solution:

1. **Differentiate both sides of the equation:**
\[ \frac{d}{dx} \left( \log(x^2 + y^2) \right) = \frac{d}{dx} \left( 2 \tan^{-1}\left(\frac{y}{x}\right) \right) \]
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