Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

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

Overview

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.

Objectives

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

• 2.7.1 Understand and know the rules for the derivatives of the e^x, a^x, ln(x), and log_a(x) functions.
• 2.7.2 Know how to combine the derivatives of the exponential and logarithmic functions with the product, quotient, and chain rules to differentiate a variety of expressions.

Terminology

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

Supplemental Resources (optional)

rev. 2020-10-20