Our purpose in this Lesson is to develop techniques of differentiation.

The derivative is the principal concept of differential calculus; it is the one single tool that we cannot omit in climbing our mountain. As with any tool, it is criticial that we learn when and how to use the derivative. Climbers must be able to use ropes, pitons, and caribiners to secure their safety on difficult climbing pitches. Even on a guided trip, each individual on the mountain must attain some degree of facility with these basic tools. The same is true for the derivative in differential calculus. The best and most expensive guides in the world can't climb the mountain for you!

Our advice for this Stage is to pay close attention, learn the basic skills of differentiation, and practice your skills until they become second nature to you.

What's Here

  • Three Basic Derivatives
  • General Rules of Differentiation
  • Derivatives of Algebraic Functions
  • Derivatives of Trigonometric Functions
  • Derivatives of Inverse Trignometric Functions
  • Derivative of the Natural Logarithm
  • Derivatives of Exponential Functions
  • Derivatives of Logarithmic Functions
  • What To Do

    The Lesson introduces the derivative and develops techniques of differentiation.

    Expected Study Time

    You will need four to five hours to go through this Lesson. You may wish to return to the Lesson later for help in completing Practice problems.


    Differentiate elementary functions.

    • Use the linearity of the derivative.
    • Use the product and quotient rules.
    • Use the chain rule.
    • Differentiate algebraic functions.
    • Differentiate trigonometric functions.
    • Differentiate exponential functions.
    • Differentiate logarithmic functions.



    © CalculusQuestTM
    Version 1
    All rights reserved---1996
    William A. Bogley
    Robby Robson