- #1
gaborfk
- 53
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Solved: Real Analysis, differentiation
If g is differentiable and g(x+y)=g(x)(g(y) find g(0) and show g'(x)=g'(0)g(x)
I solved g(0)=1
and
I got as far as
[tex]
g'(x)=\lim_{\substack{x\rightarrow 0}}g(x) \frac{g(h)-1}{h}
[/tex]
but now I am stuck.
Thank you in advance
Homework Statement
If g is differentiable and g(x+y)=g(x)(g(y) find g(0) and show g'(x)=g'(0)g(x)
The Attempt at a Solution
I solved g(0)=1
and
I got as far as
[tex]
g'(x)=\lim_{\substack{x\rightarrow 0}}g(x) \frac{g(h)-1}{h}
[/tex]
but now I am stuck.
Thank you in advance
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