Algebra I / Elem. Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems
Algebra II / E&I Algebra
Exponents & Polynomials Intermediate Algebra starts here!

Factoring Rational Expressions Rational Equations and Applications
Algebra III / Inter. Algebra
Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
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
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
Sequences and Infinite Series Power Series Vectors and Geometry of Space Vector-Valued Functions
Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
S = contains supplemental resources
Course: Calculus I
Topic: Derivatives
Subtopic: Derivatives of Exponential and Logarithmic Functions

Overview

In this lesson we learn the derivatives of ax, ln(x), and loga(x). This joins our knowledge that (ex)'=ex 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 ex, ax, ln(x), and loga(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

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 (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.

Supplemental Resources (optional)