Themes > Science > Mathematics > Calculus > Derivatives > Table Derivatives > Derivative e^x

(d/dx) e^x = e^x

Proof of (d-dx) e^x : by (d-dx) ln(x)

Given : (d-dx) ln(x) = 1/x; Chain Rule; d/dx x = 1.
Solve:

(1) (d-dx) ln(e^x) = (d-dx) x = 1
(d-dx) ln(e^x) = (d/du) ln(u) (d-dx) e^x (Set u=e^x)
= 1/u (d-dx) e^x = 1/e^x (d-dx) e^x = 1 (equation 1)
(d-dx) e^x = e^x      
Q.E.D.


Information supplied by http://www.math2.org