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The idea of the derivative of a function
The derivative of a function as the slope of the tangent line.
Derivatives of polynomials
How to compute the derivative of a polynomial.
Derivatives of more general power functions
How to compute the derivative of power functions.
A refresher on the quotient rule
How to compute the derivative of a quotient.
A refresher on the product rule
How to compute the derivative of a product.
A refresher on the chain rule
How to compute the derivative of a composition of functions.
Tangent and normal lines
How to compute the tangent and normal lines to the graph of a function.
Calculating one derivative in terms of another derivative.
Intermediate Value Theorem, location of roots
Using the Intermediate Value Theorem to find small intervals where a function must have a root.
Derivatives of transcendental functions
A list of formulas for taking derivatives of exponential, logarithm, trigonometric, and inverse trigonometric functions.
A way to simplify evaluation of limits when the limit is an indeterminate form.
The second and higher derivatives
Taking derivatives multiple times to calculate the second or higer derivative.
Inflection points, concavity upward and downward
Finding points where the second derivative changes sign.
Developing intuition about the derivative
An intuitive exploration into the properties of the derivative, illustrated by interactive graphics.
The idea of the chain rule
An illustration of the basic concept of the chain rule using interactive graphics to diagram the relevant points on the graphs and the corresponding slopes.
Simple examples of using the chain rule
Basic examples that show how to use the chain rule to calculate the derivative of the composition of functions.
Calculating the derivative of a linear function using the derivative formula
Exploring how the limit definition of the derivative gives the slope of a linear function.
The derivative of a power function
Using the limit definition of the derivative to calculate the derivative of a power function.
The quotient rule for differentiation
The quotient rule is derived from the product rule for differentiation.
Introduction to partial derivatives
The concept of partial derivatives is introduced with an illustration of heating costs. Interactive graphics demonstrate the properties of partial derivatives.