A function $f\;:\;R\rightarrow R$ satisfies the equation $f(x+y)=f(x)f(y)$ for all $x,y\in R,f(x)\neq 0.$ Suppose that the function is differentiable at $x=0$ and $f'(0)=2$.Prove that $f'(x)=2f(x).$

Share

Please log in or register to add a comment.