Problem Set 3—Simple Derivatives

Purpose

This lesson reinforces your understanding of basic rules for differentiating sums, differences, products, and quotients of powers of a variable.

Background

This exercise is mainly based on material in section 3.3 (“Differentiation Rules”) of our textbook. We covered (or will cover) this material in classes between approximately September 18 and September 26.

Activity

Solve each of the following problems:

Problem 1

Section 3.3, exercise 4 (find dw/dz and d²w/dz² given that w = 3z⁷ - 7z³ + 21z²), but also find an anti-derivative of w.

Problem 2

Find the derivative and one anti-derivative of f(x) = √x + x^-2/3.

Problem 3

Section 3.3, exercise 14a (use the product rule to find dy/dx given y = (2x + 3)(5x² - 4x)).

Problem 4

Section 3.3, exercise 24 (find du/dx given that u = (5x + 1)/2√x).

Problem 5

Section 3.3, exercise 42b (find the value at x = 1 of the derivative of u(x)/v(x) given that u(1) = 2, u′(1) = 0, v(1) = 5, and v′(1) = -1).

Follow-Up

I will grade this exercise in a face-to-face meeting with you. During this meeting I will look at your solution, ask you any questions I have about it, answer questions you have, etc. Please bring a written solution to the exercise to your meeting, as that will speed the process along.

Sign up for a meeting via Google calendar. If you worked in a group on this exercise, the whole group should schedule a single meeting with me. Please make the meeting 15 minutes long, and schedule it to finish before the end of the “Grade By” date above.