Mathematics - Continuity - Differentiability Question with Solution | TestHub

A function $f:R\to R$ satisfies the equation $f(x+y)=f(x)\cdot f(y)$ for all $\mathrm{x},\mathrm{y}$ in R and $f(x)\ne 0$ for any $x\in R$. Let the function be differentiable at $\mathrm{x}=0$ and $f^{\prime }(0)=2$ then.