f(x+y)=f(x)f(y)
f(0) =1
f\'(x)
=lim(h->0) [f(x+h) -f(x) ]/h
=lim(h->0) [f(x)f(h) -f(x) ]/h
=f(x) .lim(h->0) [f(h) -1 ]/h
=f(x) .lim(h->0) [f(h) -f(0) ]/h
=f(x).f\'(0)
ie
f\'(x)= f(x).f\'(0)
∫df(x)/f(x) =∫ f\'(0) dx
ln|f(x)| = f\'(0) .x + C
x=0
ln|f(0)| =C
C=0
ie
f(x) = e^[f\'(0).x]
