Deriving e^x

Why is the derivative of e^x also e^x? I don't understand...

Can someone post a proof?

e^x = y
Rewrite using natural log
ln y = x
Implicitly differentiate both sides
dx(ln y) = dx(x)
A bit of algebra
(1 / y)(dy/dx) = 1
dy/dx = y
dy/dx = e^x

Hope that helps.