STAGE  6:  A  TECHNICAL  CLIMB

As a limit of difference quotients, the derivative of a function computes instantaneous rates of change for the function, and also determines the existence and slopes of tangent lines to the graph of the function. It is these interpretations that make the derivative a very useful tool in a wide variety of applications.

The true miracle of the derivative occurs when it is revealed that the process of computing derivatives, called differentiation, is entirely routine. Thus, the derivative gives us the best of both worlds: It is extremely useful AND it is easy to use.

In Stage 6 we develop an extensive toolbox of differentiation techniques. Once mastered, these techniques make differentiation a routine and relatively simple task.

Objectives

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.

LESSON	What To Do: Go to the Lesson to learn new material. Go to the Practice area to develop skills and understanding. There are four Recorded Quizzes in Stage 6. There are many exercises in the Practice area. Skills developed in the Practice area for this Stage will be crucial for the Stage 6 Quizzes and throughout the rest of the course.
PRACTICE
ONWARD AND  UPWARD

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Last modified on Wednesday, 13-Sep-2000 21:28:47 PDT.