Math 161 Calculus I

Reading Outlines

You should answer these questions as you read the text.

Section 3.5

1. In Example 3 the product rule is used. On what? Which function is the u(x)? Which is the v(x)?
2. What are the product and quotient rules?
3. State the product and quotient rules for derivatives in your own words. (i.e., how are you going to remember this?)
4. If f (x) = xcos x, what is f'(x)?
5. What do you do if f (x) is the product of three other functions?
6. In Example 5, the derivative of e^-x was calculated correctly. What is wrong with the following argument? Since e^-x = ${\frac{1}{e^x}}$, and since the derivative of the top is 0 and the derivative of the bottom is e^x, the derivative of e^-x is ${\frac{0}{e^x}}$ = 0.
7. Clearly explain each step of the calculation needed to take the derivative of ${\frac{x}{e^x\sin x}}$ in Example 10 -- fill in all the steps which were left out.