**Tangent Lines**- Tutorial on tangent lines as an introduction to the derivative.
- A LiveMath notebook illustrating the tangent line as the limit of secant lines.
- A JavaScript exploration of the numerical estimates of the slope of the tangent line to the graphs of various functions.
- An animation demonstrating the estimation of the slope of the tangent by zooming in.
- A LiveMath notebook which compares graphically a function with its linear approximation.
- Javascript module which compares numerically a function with its linear approximation.
- Computer programs that graphically illustrate the tangent line as the limit of secant lines. Also,
- TI-86 Graphing Calculator [Using Flash]
- TI-85 Graphing Calculator

- Another computer program that graphically illustrates the tangent line as the limit of secant lines.
- Computer programs that plot a tangent line to the graph of a given function. Also,
- TI-86 Graphing Calculator [Using Flash]
- TI-85 Graphing Calculator

- Another computer program that plots the graph of a function together with the tangent line at a given point.

**Linear Approximations**- Tutorial on the accuracy of a linear approximation.
- A LiveMath Notebook which can be used to determine accuracy of using a linear approximation.
- Computer programs that can be used to determine accuracy of using a linear approximation. Also,
- TI-86 Graphing Calculator [Using Flash]
- TI-85 Graphing Calculator

**Definition of Derivative at a Point**- Tutorial on the definition of derivative at a point.
- Using the definition of derivative at a point, calculate the derivative of a quadratic at a point.

[Using HotEqn] [Using IBM Techexplorer] [Using IBM Pro.Techexplorer] - Using the definition of derivative at a point, calculate the derivative of a square root of a function at a point.

[Using HotEqn] [Using IBM Techexplorer] [Using IBM Pro.Techexplorer] - Using the definition of derivative at a point, calculates the derivative of a rational function at a point.

[Using HotEqn] [Using IBM Techexplorer] [Using IBM Pro.Techexplorer] - A LiveMath Notebook illustrating how to use the definition of derivative to calculate the derivative of a quotient at a specific point.
- A LiveMath Notebook which, using the definition of derivative at a point, investigates the derivative of
**x**at^{2/3}**x = 0**. - A LiveMath Notebook illustrating how to use the definition of derivative to calculate the derivative of a radical at a specific point.
- Computer programs that numerically investigate the behavior of the Newton quotient of a function at a point.
- Computer programs that numerically investigate the behavior of the Newton quotient of a function at a point. In this case, the function is not differentiable at the given point.
- Computer programs that numerically investigate the behavior of the Newton quotient of a function at a point. In this case, the function is not differentiable at the given point but the limit of the symmetric difference quotient exists.

- Using the definition of derivative at a point, calculate the derivative of a quadratic at a point.
**Definition of Derivative**- Tutorial on the definition of derivative.
- Using the definition of derivative, calculate the derivative of a quadratic at a point.

[Using HotEqn] [Using IBM Techexplorer] [Using IBM Pro. Techexplorer] - Using the definition of derivative, calculate the derivative of a square root of a function at a point.

[Using HotEqn] [Using IBM Techexplorer] [Using IBM Pro. Techexplorer] - Using the definition of derivative, calculate the derivative of a rational function at a point.

[Using HotEqn] [Using IBM Techexplorer] [Using IBM Pro. Techexplorer] - A LiveMath Notebook illustrating how to use the definition of derivative to calculate the derivative of a quadratic.
- A LiveMath Notebook illustrating how to use the definition of derivative to calculate the derivative of a quotient.
- A LiveMath Notebook illustrating how to use the definition of derivative to calculate the derivative of a radical.
- Drill problems for finding the derivative of a function using the definition of a derivative.

- Using the definition of derivative, calculate the derivative of a quadratic at a point.
**Differentiation Formulas**- Tutorial on elementary differentiation formulas, their derivation and use. Includes the Power Formula.
- A LiveMath Notebook illustrating how to use the definition of derivative to obtain the power rule.
- A LiveMath Notebook illustrating the use of the formula for the derivative of a sum.

**Derivative of the Exponential Function**- Tutorial on the calculation of the derivative of the exponential function.
- A LiveMath notebook illustrating the finding of the derivative of an exponential function at
**x = 0**. - JavaScript exploration of the numerical estimates of the slope of the tangent line to the exponential function.

- A LiveMath notebook illustrating the finding of the derivative of an exponential function at
**Product Rule**- Tutorial on the Product Rule.
- A LiveMath notebook which illustrates the use of the product rule.
- Drill problems for differentiation using the product rule. (Algebraic and exponential functions).

**Quotient Rule**- Tutorial on the Quotient Rule.
- A LiveMath notebook which illustrates the use of the quotient rule.
- Drill problems for differentiation using the quotient rule.

**Derivatives of the Trigonometric Functions**- Tutorial on the calculation of the derivatives of the trigonometric functions.
**The Chain Rule**- Tutorial on the Chain Rule.
- A LiveMath notebook illustrating the use of the chain rule.
- Drill problems for differentiation using the chain rule.
- Computer program that graphically illustrates the chain rule.

**Derivatives of Functions**-
- A list of differentiation formulas.
- Drill problems for differentiation using the product rule.
- Quiz on finding the derivative of functions.
- Using the TI85 graphing calculator to plot approximating the graph of a derivative with the Newton quotient.