- 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,
- 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,
- 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,
- 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
-