Algebra I / Elem. Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems
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Exponents & Polynomials Intermediate Algebra starts here!

Factoring Rational Expressions Rational Equations and Applications
Algebra III / Inter. Algebra
Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
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Calculus I
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S = contains supplemental resources
Course: Calculus I
Topic: Derivatives
Subtopic: Product Rule, Quotient Rules, & Deriv. of Trig Functions

Overview

If we wish to take a derivative of, for example, x/sinx, we need a rule for taking the derivative of a quotient. Not surprisingly, there is one, and it is called the quotient rule. That along with the product rule, which finds the derivative of a produce such as xex, allow up to find the derivatives of the remaining four trigonometric functions.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 2.4.1 Apply the product rule to differentiate a product
• 2.4.2 Apply the quotient rule to differentiate a quotient
• 2.4.3 Know the derivative of all six trigonometric functions
• 2.4.4 Find the slope and equation of a tangent line to a function involving a product or quotient function using the derivative without using the formal definition of derivative

Terminology

Define: product rule, quotient rule

Text Notes

• The product rule and quotient rule are important to memorize! There are songs that serve as mnemonics for them posted on YouTube if you want to check them out.
• Be sure that you can apply the quotient rule to the ratio identities for the trig functions tan(x), cot(x), sec(x), and csc(x) to find their derivatives.

Supplemental Resources (optional)