Search Menu

Contents

Derivatives of ex and of the Natural Log

page 1 of 3

Derivatives of ex and of the Natural Log

Derivatives of ex and of the Natural Log

Derivatives of ex and of the Natural Log

Derivatives of ex and of the Natural Log

Derivatives of ex and of the Natural Log

Derivatives of Exponential Functions

One truly remarkable characteristic of e x is that

e x = e x    

Besides the trivial case of f (x) = 0 , e x and its constant multiples are the only functions whose derivatives are equal to themselves!

Incorporating the principles of the chain rule, we might also say that if u is a function of x , then

e u = e u    

By extension, e x dx = e x + c . Using the fact that

e u = e u    

we can derive a more general formula for the derivative of a x , where a is any positive constant.

First, note that a x can be rewritten as