Inverse, Exponential, and Logarithmic Functions

Topics

Inverse, Exponential, and Logarithmic Functions Derivatives of e x and of the Natural Log

Save

Topics Inverse, Exponential, and Logarithmic Functions Derivatives of e x 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^xdx = 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

Previous section Next page Derivatives of e x and of the Natural Log page 2

Take a Study Break