Differentiation of $g(x)=f(x+c)$ 
Suppose $g(x)=f(x+c)$.
Prove $g'(x)=f'(x+c)$

I know that $$g'(x)=\lim_{x\to 0} \frac{g(x+h)-g(x)}{h}$$ that is it please help.

$$f'(x+c)= \lim_{h\to0}\frac{f(x+c+h)-f(x+c)}{h}=\lim_{h\to0}\frac{g(x+h)-g(x)}{h}=g'(x)$$
All that is done is a substitution of $g(x)=f(x+c)$
