Tangent Lines

Tutorial on tangent lines as an introduction to the derivative.

Linear Approximations

Tutorial on the accuracy of a linear approximation.

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 x2/3 at 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.

Definition of Derivative

Tutorial on the definition of derivative.

Differentiation Formulas

Tutorial on elementary differentiation formulas, their derivation and use. Includes the Power Formula.

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.

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.
• Drill problems for differentiation using the product rule. (Emphasis on trigonometric functions).
• Drill problems for differentiation using the quotient rule. (Emphasis on trigonometric functions).

The Chain Rule

Tutorial on the Chain Rule.

Derivatives of Functions