Study Guide

Computing Derivatives

Computing Derivatives Introduction

We've already been through the formal derivative definition. Sure, it's fun to be formal once in a while. Have a meal way better than the cafeteria offers. Maybe hop a ride in a with a knife and fork. Seriously, who wants to do that everyday? It's time to cut loose (footloose?). Even better, it's time to cut some calculus corners. In this section we'll discuss the cheat codes...or rules...for computing derivatives. The rules allow us to skip ahead of the level that uses limits, into the level where more complicated functions can be conquered. There are rules for many different function scenarios, so learn them and be a calc champ.

When we compute derivatives, we're mostly doing mechanical computations. After we've learned all the rules and have practiced enough, we'll be able to compute the derivatives of most functions we'll encounter almost without thinking. Of course there are reasons along with the rules, and understanding the reasons will probably make memorizing the rules more...memorable.

Computing Derivatives Resources


Table of Derivatives
When it comes to basic derivatives, this is the last table you’ll ever need. Instead of deriving them using the tedious limit formula, you can just look them up here.

Rules of Differentiation
If you ever forget low-dee-high minus high-dee-low over low-low, you can always look up the quotient rule in a less phonetically terrifying form.

Chain Rule Examples
The chain rule isn’t a leash that your teacher uses to train you. Here are some examples that demonstrate how to use the chain rule.

Tutorial on Chain Rule
Like a shape-shifter constantly changing forms, the chain rule can be applied in several different notations. Learn how the chain rule is applied in all notations.


Chain Rule Examples Explained
The chain rule is a powerful, time-saving tool. It’s the calculus equivalent of using a jack-hammer to break concrete over using a hammer and chisel. This video shows you why.

Quotient Rule Example
High-low, high-low, to the quotient rule we go. With low-dee-high minus high-dee-low, divide by low-low and a new derivative you will know.

Product Rule Explained
The product rule isn’t a guide on how to increase your sales of purple desk chairs. It’s an easy-to-use rule to simplify complicated problems involving derivatives. If you pay close attention in this video, you’ll find an easy way to avoid using the quotient rule by using the product rule instead.

Implicit Differentiation – Basic Ideas and Examples
Yeah, we know. Implicit differentiation is terrible. You just wish it’d come out and explicitly ask you on a date. It’s so wrapped up its own little equation that it can’t. You’ll learn how to derive the derivative from it implicitly here.

Games and Tools

Quotient Rule Tool
Sometimes, the quotient rule can leave you with a mess of numbers and letters floating around like an alphanumeric soup. Here’s a calculator to compute derivatives using the quotient rule, with step by step explanations. We hope it tastes as good as tomato soup once you figure out what you have left on paper.

Implicit Differentiation Calculator
This calculator will give you a way to explicitly check the implicit derivative of your equation. Pretty cool. Soon, computers will be able to fetch balls for you.