Page 85 - Calculus Workbook For Dummies

Chapter 6

Rules, Rules, Rules:

The Differentiation Handbook

In This Chapter

Boning up on basic derivative rules
Producing your quota of product and quotient problems
Joining the chain rule gang
Achieving higher order differentiation

hapter 5 gives you the meaning of the derivative. In this chapter, you practice rules for
Cfinding derivatives. But before you practice the following rules, you may want to go
back to the Cheat Sheet in Calculus For Dummies or to your calc text to review the basic
derivatives. For example, you need to know that the derivative of sine is cosine.

Rules for Beginners

Okay, now that you’ve got the memorization stuff taken care, you now begin some rules that
involve more than just memorizing the answer.
First there’s the derivative of a constant rule: The derivative of a constant is zero. Alright —
this one’s also just memorization.

And then there’s the power rule: To find the derivative of a variable raised to a power, bring
the power in front — multiplying it by the coefficient, if there is one — then reduce the
power by one.

Q. What’s the derivative of 5x ? In fact, there’s no reason to write this
3
interim step down at all. I do it simply to
A. 15x 2 make the process clear.
2. Reduce the power by one.
1. Bring the power in front, multiplying it
2
by the coefficient. This gives you the final answer of 15x .
3
So far you’ve got 15x . Note that this
3
does not equal 5x and so you should
not put an equal sign in front of it.