Section 3.3 Worksheet: Differentiation formulas

Assigned problems: Exercises pp. 156-158, #4, 13, 17, 24, 32, 44, 60, 63, 80 (due Tuesday, 2/11)

1. How would you say the Sum Rule and the Difference Rule in words? Are the product and quotient rules equally intuitive?

2. The power rule is the rule most students associate with differentiation. State the power rule in words.

3. State the quotient rule in words, and give an example of its use.

4. State the product rule in words, and give an example of its use. Give an example that demonstrates that the derivative of a product is not simply the product of the derivatives.

5. Once you know the product rule and that the derivative of a constant function is zero, you can deduce the constant multiple rule. How?

Notes:

1. Let me remark that many students seem to think of the differentiation formulas as fundamental, rather than as simple consequences of fundamental theorems. The formulas are mechanical; the understanding is not. I prefer that you understand the idea of the derivative as a limit, or slope of a tangent line, rather than mindlessly memorize differentiation formulas. These your computer is very capable of spitting out: it is the understanding of the underlying concepts which is the human forte.
2. The second proof of the Power Rule (p. 148) makes use of the binomial theorem. Recall that Newton spent the ``plague years'' around 1666 developing this idea, among others.