Dave's Math Tables: Derivative e^x
(Math | Calculus | Derivatives | Table Of | 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.

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