Unit route
Study lessons in order, complete the pathway selected by diagnostic evidence, conduct the investigation, then demonstrate mastery. Reassessment follows correction and reflection.
Weeks 16, 17, 18 · 8 detailed lessons
Chain Rule, Implicit & Inverse Functions
How do nested, implicit, and inverse relationships change the way derivatives are calculated and interpreted?
Pathways
Lesson 01 · Week 16
Chain Rule Concept and Structure
The chain rule differentiates a composition by multiplying the rate of the outer function with the rate of the inner function. Clear layer identification prevents missing factors.…
Lesson 02 · Week 16Chain Rule with Polynomial and Rational Compositions
The chain rule differentiates a composition by multiplying the rate of the outer function with the rate of the inner function. Clear layer identification prevents missing factors.…
Lesson 03 · Week 16Chain Rule with Trigonometric Compositions
The chain rule differentiates a composition by multiplying the rate of the outer function with the rate of the inner function. Clear layer identification prevents missing factors.…
Lesson 04 · Week 17Chain Rule with Exponential and Logarithmic Compositions
The chain rule differentiates a composition by multiplying the rate of the outer function with the rate of the inner function. Clear layer identification prevents missing factors.…
Lesson 05 · Week 17Implicit Differentiation
Implicit differentiation treats y as a function of x even when the relation is not solved for y. Every derivative of a y-expression carries a dy/dx factor.…
Lesson 06 · Week 17Second Derivatives of Implicit Relations
Implicit differentiation treats y as a function of x even when the relation is not solved for y. Every derivative of a y-expression carries a dy/dx factor.…
Lesson 07 · Week 18Derivatives of Inverse and Inverse Trigonometric Functions
The derivative of an inverse reverses input and output while taking the reciprocal of the original slope at the corresponding point. A zero original slope prevents a finite inverse derivativ…
Lesson 08 · Week 18Logarithmic Differentiation
Logarithmic differentiation is useful when variables appear in both bases and exponents or when products and quotients contain many factors. Taking logarithms turns multiplicative structure …