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Differentiation: The quotient rule

Differentiation: The quotient rule preview
Differentiation: The quotient rule preview
Differentiation: The quotient rule video preview 2
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Look Inside · 9 pages

Opening slide for Differentiation: The quotient rule, stating the goal of differentiating quotients of functions
Opening slide and lesson objective
Derivative review slide covering the constant, power, sum or difference, constant multiple, and product rules
Review of five differentiation rules
Quotient rule introduction using x⁶/x⁴ to show why dividing derivatives does not differentiate a quotient
Introduction to why a quotient needs its own rule
First quotient rule derivation slide, using the limit definition, subtracting fractions, and regrouping terms
First part of the derivation from first principles
Second quotient rule derivation slide, factoring terms and evaluating limits to obtain (gf′ − fg′)/g²
Second part of the derivation and resulting formula
Quotient rule reference slide presenting the derivative of f(x)/g(x) in prime notation and d/dx notation
Formula reference using two derivative notations
Worked example 1 differentiates y = 4x/(x² + 1), applying the quotient rule and simplifying the result
Worked example 1: a linear numerator
Worked example 2 finds the derivative of h(x) = (x² + 1)/(x + 1), with x ≠ −1, and simplifies the result
Worked example 2: a linear denominator
Worked example 3 differentiates y = (x² − 3)/(3x − x²), expanding products and canceling cubic terms
Worked example 3: two quadratic expressions
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Grade 12

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About This Product

Differentiation: The quotient rule is a PowerPoint resource designed to help high school calculus students learn how to find the derivative of a quotient of functions. This 10 slide presentation clearly explains the quotient rule for differentiation, providing step-by-step instructions and examples. Educators can use this resource when introducing the quotient rule to the whole class or in small groups. It also makes a useful review or homework assignment. Walking through the slides, students will understand how to take the derivative of a fraction using the quotient rule. With informative visuals and concise explanations written at a grade 7-8 reading level, this teaching resource aims to break down this essential calculus concept for improved comprehension and retention.

What's Included

PowerPoint presentation, 10 slides

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