Calculus problem

[Samjohn]

Hello,
this is a homework problem that I tried to work my way through but did not succeed.
Let f(x) be differentiable function with the properties that f(0)=1, f'(0)=1, and that f(a+b)=f(a)f(b) for all a and b. show that f'(x)=f(x) for all x and deduce that f(x)=e^x. (Hint: use the definition of the derivative of a function f(x)).

Here is what I did:

 

[Deleted member 4993]

Let f(x) be differentiable function with the properties that f(0)=1, f'(0)=1, and that f(a+b)=f(a)f(b) for all a and b. show that f'(x)=f(x) for all x and deduce that f(x)=e^x. (Hint: use the definition of the derivative of a function f(x)).

Please share your work with us .

If you are stuck at the beginning tell us and we'll start with the definitions of differentiable function

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[stapel]

How did you get from your first line to your second? How did you get from your second line to your third.

This time, please REPLY with your working, rather than editing the initial post. That way, the rest of us can follow the conversation. Thank you!