Differentiation Rule Selector

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Description

This interactive decision tree helps students develop metacognitive awareness when selecting differentiation techniques. Instead of blindly applying rules, students learn to systematically evaluate the structure of a function to determine the most efficient differentiation approach.

How It Works

Start at the top with a function you want to differentiate
Answer Yes or No to each question about the function's structure
Follow the highlighted path through the decision tree
Arrive at the appropriate rule with formula and example

Decision Tree Logic

The tree guides students through these key questions:

Question	If Yes	If No
Is it a single term (no + or -)?	Check if it's power form	Check for sum/difference
Is it cx^n form?	Use Power Rule	Check for composition
Is it a sum/difference?	Use Sum/Difference Rule	Check for product
Is it a composition f(g(x))?	Use Chain Rule	Use special function rules
Is it a product of functions?	Use Product Rule	Use Quotient Rule

Visual Features

Pulsing current node shows where you are in the decision process
Highlighted path traces your choices through the tree
Color-coded terminal nodes distinguish different rules
Info panel shows examples and formulas for the current rule

Delta Moment

"Before I roll down any curve, I need to know what I'm dealing with. Is it a simple slope? A product of terrains? This decision tree is like my GPS for derivatives - it helps me choose the right tool before I start calculating!"

Lesson Plan

Learning Objectives

By the end of this activity, students will be able to:

Evaluate function structure to identify appropriate differentiation techniques
Select the most efficient rule from Power, Sum/Difference, Product, Quotient, and Chain rules
Justify their rule selection based on function characteristics

Grade Level

High School (AP Calculus AB/BC) and Undergraduate Calculus I

Duration

15-20 minutes for introduction; can be used repeatedly as a reference tool

Prerequisites

Students should be familiar with:

Basic derivative rules (power, constant multiple)
Sum and difference rules
Product and quotient rules
Chain rule
Special function derivatives (trig, exponential, logarithmic)

Activities

Activity 1: Guided Exploration (10 minutes)

Have students work through these functions using the decision tree:

f(x) = 5x^3 (Power Rule)
f(x) = x^2 + 3x - 7 (Sum/Difference Rule)
f(x) = x^2 sin(x) (Product Rule)
f(x) = sin(x^2) (Chain Rule)
f(x) = x/(x+1) (Quotient Rule)

Activity 2: Rule Justification (10 minutes)

For each function below, have students: 1. Use the decision tree to find the rule 2. Write down the path they took (e.g., "Q1(N) -> Q2(Y) -> Sum Rule") 3. Explain WHY each answer led them down that path

Function	Expected Rule
(2x+1)^4	Chain Rule
e^x cos(x)	Product Rule
4x^{-2} + 3x	Sum Rule, then Power Rule
tan(x)/x	Quotient Rule

Activity 3: Create Your Own (5 minutes)

Students create one function for each terminal rule and verify using the decision tree.

Assessment

Quick Check Questions:

What is the FIRST question you should ask about any function before differentiating?
How do you distinguish between when to use Product Rule vs. Chain Rule?
Why is identifying "single term" vs "multiple terms" the first decision point?

Exit Ticket:

Given f(x) = x^2 e^{3x}, trace through the decision tree and explain each choice. Then compute the derivative.

Differentiation Strategies

For struggling students: Start with simpler functions that clearly fit one category
For advanced students: Present functions that require multiple rules (e.g., chain + product)