We define the function exp(x) by
These two facts imply
(the derivative of each term is its predecessor)
exp(1) = e = 2.71828
1. exp(0) = 1, exp(1) = e
2. exp(u + v) = exp(u)exp(v)
3. exp(uv) = (exp(u))v
Applying the third property to u = 1 and using the first, we get exp(v) = ev.
From now on, we will use the power notation expressed in this formula for the exponent function.
Proof of 2
Proof of 3
Proof of 4