Math Insight

Pages similar to: The idea of the product rule

• A refresher on the product rule
  How to compute the derivative of a product.
• A refresher on the quotient rule
  How to compute the derivative of a quotient.
• A refresher on the chain rule
  How to compute the derivative of a composition of functions.
• 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.
• The quotient rule for differentiation
  The quotient rule is derived from the product rule for differentiation.
• 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.
• Related rates
  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.
• Newton's Method
  A method to approximate the roots to an equation.
• Derivatives of transcendental functions
  A list of formulas for taking derivatives of exponential, logarithm, trigonometric, and inverse trigonometric functions.
• L'Hospital's rule
  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.
• Approximating a nonlinear function by a linear function
  The secant line and tangent line are two ways to approximate a nonlinear function by a linear one.
• Developing intuition about the derivative
  An intuitive exploration into the properties of the derivative, illustrated by interactive graphics.
• Exploring the derivative of the exponential function
  A guided tour into the reasons that the derivative of the exponential function with base e is the function itself.
• The derivative of the natural logarithm
  Determining the derivative of the natural logarithm from the fact that it is the inverse of the exponential function.

Back to: The idea of the product rule