Can you derive the exponential property $ [f(x+y) = f(x)\cdot f(y)]$ from $y' = y$?
Prove that if $f(t)$ satisfies $f(t)=f'(t)$, then $f(t+s)=f(t)f(s)$ for all $t,s\in R$ without using the fact that $f(t)=c\cdot e^t$.