Math 161 Calculus I

Reading Outlines

You should answer these questions as you read the text.

Section 3.6

1. What is the chain rule?
2. Why do we need the chain rule? When is it appropriate to use the chain rule?
3. Explain in your own words how to use the chain rule to take the derivative of ``nested'' functions.
4. Let k(x) = cos(x³). This function is a composition of two functions f and g. What are they? What is k'(x)?
5. Explain the ``Why a product?'' paragraph on page 225.
6. In Example 1, the book states that ``composition isn't commutative''. What does this mean?
7. The chain rule is used twice in Example 3. Carefully explain the computation by explicitly stating where and how the chain rule is used.
8. What do they mean by ``Differentiable functions are almost linear'' (page 228)?
9. Specifically, how are the derivatives of inverses functions related? How does the picture at the top of page 203 illustrate this? Use the picture to explain why we evaluate the derivative of f at g(x).
10. Why is finding antiderivatives so much harder than finding derivatives?