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This graphic presentation illustrates the relationship between the shape of a function and the sign of the first derivative.

Differentiation: General Applications, One-Variable Calculus

The Product Rule

Wolfram's demo for the product rule, with dropdown menus for the functions. Users can download the free Mathematica Player to play a live version of the demo.

Differentiation: Calculation Rules

Illustrating the Washer Method

Java applet allows the user to visualize the washer method for finding the volume of a solid formed by revolving a specific region about the \(x\)-axis.

Integration: Applications

Combinations: Product and Quotient

Three adjacent windows display graphs of (1) a function \(f\) and its derivative, (2) a function \(g\) and its derivative, and (3) a function \(h\) and its derivative.

Differentiation: Calculation Rules, One-Variable Calculus

Derivatives of Quintic Polynomials

Wolfram's demo for the first four derivatives of a fifth degree polynomial, with sliders for the coefficients of the polynomial and a particular value of \(x\).

Differentiation: Calculation Rules

Power Functions

Two adjacent windows display graphs of (1) a function \(f\) and a tangent line, and (2) the derivative \(f '\).

Differentiation: Calculation Rules, One-Variable Calculus

MSOffice Math

MSOffice Math is a free add-on to the MSWord2007 that allows the user to insert editable math notation, to simplify algebraic expressions, to solve equations, to differentiate or integrate functio

General Tools

Product and Quotient Rules

This site includes descriptions and examples of the Product Rule, the Reciprocal Rule, and the Quotient Rule.

Differentiation: Calculation Rules

The Chain Rule

Wolfram's demo for the chain rule, with a selection of possible "inside" and "outside" functions, and sliders for specifying a value of \(x\) and for adjusting the scales of plots showing graphs o

Differentiation: Calculation Rules

The Chain Rule

Wolfram's MathWorld has descriptions of the chain rule, both single variable and multivariable versions.

Differentiation: Calculation Rules