Derivative of Exponential function

Let y=f(x)= e x , then dy dx = lim h0 f(x+h)f(x) h

= lim h0 e x+h e x h

= lim h0 e x e h e x h

= lim h0 e x ( e h 1) h

= lim h0 e x ( e h 1) h

=( e x ) lim h0 e h 1 h

=( e x )(1)

= e x

In the above, we have used the fact that lim h0 e h 1 h =1