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## Real Analysis, differentiation

1. The problem statement, all variables and given/known data
If g is differentiable and g(x+y)=g(x)(g(y) find g(0) and show g'(x)=g'(0)g(x)

3. The attempt at a solution
I solved g(0)=1

and

I got as far as

$$g'(x)=\lim_{\substack{x\rightarrow 0}}g(x) \frac{g(h)-1}{h}$$

but now I am stuck.