Let $f$ be a differential function satisfying the relation $f(x+y)=f(x)+f(y) - 2xy + (e^x -1)(e^y -1)$$ \ \forall x , y \in\mathbb R $ and $f'(0)=1$
My work
Putting $y=0$ $$f(x)=f(x) + f(0)$$
$$f'(x)=\lim_{h\to 0} \frac{f(x+h)-f(x)}{h}$$ $$f'(x)=\lim_{h\to 0} \frac{f(x)+f(h) - 2xh + (e^x -1)(e^h -1)-f(x)}{h}$$ $$f'(x)=\lim_{h\to 0} \frac{f(h) - 2xh + (e^x -1)(e^h -1)}{h}$$ How to predict things after that?