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Find function f(x) which is differentiab...

Find function f(x) which is differentiable and satisfy the relation `f(x+y)=f(x)+f(y)+(e^(x)-1)(e^(y)-1)AA x, y in R, and f'(0)=2.`

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To find the function \( f(x) \) that is differentiable and satisfies the relation \[ f(x+y) = f(x) + f(y) + (e^x - 1)(e^y - 1) \] for all \( x, y \in \mathbb{R} \), and given that \( f'(0) = 2 \), we can follow these steps: ...
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