Course: Calculus I
Topic: Derivatives
Subtopic: Derivatives of Exponential and Logarithmic Functions


In this lesson we learn the derivatives of `a^x`, `ln(x)`, and `log_a(x)`. This joins our knowledge that `d/dx(e^x)=e^x` to complete our list of derivatives of the exponential and logarithmic functions.


By the end of this topic you should know and be prepared to be tested on:


Terms you should be able to define: natural exponential function, general exponential function, natural logarithmic function, general logarithmic function

Memorize! these derivatives. They are extremely common and useful.

Text Notes

Different texts derive the formula for 'd/dx(ln x)` in different ways. Your text may use the inverse function theorem or find the derivative implicitly. Either way works but you should compare both methods to be sure that they make sense.

Mini-Lectures and Examples

STUDY: Derivatives - Exponential, Logarithmic, Inverse, and Inverse Trig Functions

Supplemental Resources (optional)

Video: e^x and ln(x), Selwyn Hollis's Video Calculus

Lesson: Using the Chain Rule, Dale Hoffman's Contemporary Calculus

rev. 2020-10-20