Let f and g be two functions whose domains are the set of all real numbers. Furthermore, suppose that
g(x) = x f(x) + 1
g (a+b) = g(a) g(b) for all a and b
lim f(x) = 1
x-> 0
See if by using the given you can get: $\displaystyle \dfrac{g(x+h)-g(x)}{h}=\dfrac{xhf(x)f(h)+hf(h)}{h}.$