National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Derivation of De Moivre's Formula
A formula using Euler's formula to derive DeMoivre's theorem. Basic calculus skills of differentiating and integrating are required to understand this explanation.
Stefan Warner and Steven R. Costenoble
Finite Mathematics & Applied Calculus: Using and Deriving Algebraic Properties of Logarithms
The resource investigates how to use and derive algebraic properties of logarithms. Students learn about the concepts through notes and examples. Practice problems are included.
Other
Karl's Calculus Tutor: Derivatives More Rules
This site provides a detailed overview of the quotient rule, as derived from the product rule. Content includes examples and exercises.
Stefan Warner and Steven R. Costenoble
Finite Mathematics & Applied Calculus: Topic Summaries: Trigonometric Functions
The topic summary outlines trigonometric functions. Some topics reviewed are derivatives of trigonometric functions, sine function, trigonometric identities, and indefinite integrals of trigonometric functions. The resource consists of...
Paul Dawkins
Paul's Online Notes: Calculus Iii: Multiple Integrals
The resource examines applications of partial derivatives. Topics investigated are double integrals, triple integrals, surface area, and iterated integrals. Class notes, definitions, and examples with detailed solutions are included. The...
BBC
Bbc: Differentiations
This site presents a tutorial on the topic of differentiation. Points of focus include rules for differentiation, tangents to curves, derivatives, increasing and decreasing functions, and optimization. Examples and a practice test are...
Texas Instruments
Texas Instruments: Using Traffic Data to Reinforce Inflection Points in Calculus
Real data from the morning rush on the Chicago expressways is the basis for a piece-wise regression. The students' success depends on their understanding of inflection points. Students need to use the Select command to split the data...
Lawrence Hall of Science
The Math Page: An Approach to Calculus: Instantaneous Velocity and Related Rates
Here is a site that clearly and thoroughly explains instantaneous velocity and how to solve related rates problems by using implicit differentiation. There are example problems solved, problems for the student to attempt, and answers to...
Stefan Warner and Steven R. Costenoble
Finite Mathematics & Applied Calculus: Topic Summaries: Techniques of Differentiation
The topic summary outlines techniques of differentiation. Some topics reviewed are product rule, quotient rule, chain rule, and implicit differentiation. The resource consists of definitions, notes, and examples.
Virginia Commonwealth University
Virginia Commonwealth University: Inverse Function
This page from the Virginia Commonwealth University is a slide with a short definition of the inverse function and its' derivative. It provides formulas.
Khan Academy
Khan Academy: Worked Example Motion Problems With Definite Integrals
Remember, anti derivative of acceleration with respect to time is velocity and anti derivative of velocity with respect to time is distance where acceleration, velocity, distance are all functions of t, the time. This concept is very...
Math Medics
S.o.s. Math: The Chain Rule
Finding derivatives by using the chain rule is explained through examples in this tutorial.
Department of Defense
Do Dea: Optimization Business Applications
You can apply calculus to the business world! This lesson goes through a number of business applications of derivatives and optimization that are widely used. Explanations and examples are provided. Great review for the AP Calculus test!
University of Minnesota
University of Minnesota: How Does Light Travel?
Contains a four step procedure to deriving the law of reflection using algebra, Fermat's principle, and calculus (simple derivatives). This is good for an in-class theoretical exercise.
Department of Defense
Do Dea: Marginal Cost, Marginal Revenue
Business applications of derivatives are widely used. Marginal revenue, cost, and profit functions that you can find by taking the respective derivatives of revenue, cost, or profit would provide very valuable information to a business....
Department of Defense
Do Dea: Optimization the Basics
In this lesson, you learn how to apply the concepts of maxima and minima to any formula that is generated by business, economics, physics, etc. It is one of the most important applications of derivatives and will show up on your AP...
Department of Defense
Do Dea: Optimization Examples
Practice types of problems you will see on AP Calculus test that deal with optimization. Formulas and examples are provided.
Analyze Math
Analyze Math: Differentiation of Logarithmic Functions
Students investigate the derivatives of logarithmic functions. The resource includes examples and practice problems with solutions.
Stefan Warner and Steven R. Costenoble
Finite Mathematics & Applied Calculus: Function Evaluator and Grapher
Students enter functions into the grapher. The resource allows students to compute derivatives, graph derivatives, trace curves, compute function values, and add plotted points.
Wolfram Research
Wolfram Math World: Product Rule
This MathWorld site explains the process of taking a derivative, in particlar the derivative of a product. The page begins by showing the concept of taking a derivative using mathematical notation, and breaking the result into component...
Wolfram Research
Wolfram Science World: Cl Circuit
Shows how simple harmonic motion is used in a circuit comprised of an inductor and a capacitor. Includes detailed formula derivation utilizing calculus.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Volume Equations for a Sphere and Pyramid
This site uses calculus to explain how the formulas for finding the volume of a sphere and a pyramid were derived.
Texas Instruments
Texas Instruments: Zeros of a Cubic
This activity involves some of the prerequisites of calculus relating to functions and equations. It also contains an application of differentiation. (Continued. See "before the activity.")