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Let f: R-{0}rarrR be a function which is...

Let `f: R-{0}rarrR` be a function which is differentiable in its domain and satisfying the equation `f(x+y)=f(x)+f(y)+(x+y)/(xy)-(1)/(x+y),` also f'(1)=2. Then find the function.

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To find the function \( f(x) \) that satisfies the given functional equation and the derivative condition, we will follow a systematic approach. ### Step 1: Analyze the Functional Equation The functional equation given is: \[ f(x+y) = f(x) + f(y) + \frac{x+y}{xy} - \frac{1}{x+y} \] We can rearrange this equation to isolate \( f(x+y) \): ...
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