Episode Synopsis "Chapter 3.6: The Chain Rule - 12) Quotient, then Chain Rule"

Chapter 3.6: The Chain Rule

Listen "Chapter 3.6: The Chain Rule - 12) Quotient, then Chain Rule"

More episodes of the podcast Precalculus & Elements of Calculus (Chapter 3) - Course

• Chapter 3.10: Related Rates - 01) Related Rates: Shuttle Launch
• Chapter 3.10: Related Rates - 02) Shuttle Launch, Part II
• Chapter 3.10: Related Rates - 03) Oil Spill
• Chapter 3.10: Related Rates - 04) Shadows and Similar Triangles
• Chapter 3.11: Newton's Method - 01) Newton's Method
• Chapter 3.11: Newton's Method - 02) Newton's Method on Excel
• Chapter 3.11: Newton's Method - 03) Newton's Method on TI-89
• Chapter 3.1: Slope of a Curve - 01) Introduction
• Chapter 3.1: Slope of a Curve - 02) Intro. (Cont’d) and Average Rate of Change
• Chapter 3.1: Slope of a Curve - 03) Average Rate of Change (Cont’d)
• Chapter 3.1: Slope of a Curve - 04) Ave. and Instantaneous Rate of Change
• Chapter 3.1: Slope of a Curve - 05) Approximating Instantaneous Rate of Change, Part I
• Chapter 3.1: Slope of a Curve - 06) Approximating Instantaneous Rate of Change, Part II
• Chapter 3.1: Slope of a Curve - 07) Approximating Instantaneous Rate of Change, Part III
• Chapter 3.1: Slope of a Curve - 08) Introduction to Slope of Curve/Tangent Line
• Chapter 3.1: Slope of a Curve - 09) Slope of Secant Approximating Slope of Tangent
• Chapter 3.1: Slope of a Curve - 10) The Slope as a Limit
• Chapter 3.1: Slope of a Curve - 11) Finding Slope of Tangent to a Curve at a Point
• Chapter 3.1: Slope of a Curve - 12) Finding Slope to Curve (Cont’d)
• Chapter 3.1: Slope of a Curve - 13) Finding Slope of Tangent, Example 2
• Chapter 3.1: Slope of a Curve - 14) Finding Slope of Curve at 4 Different Points
• Chapter 3.1: Slope of a Curve - 15) Slope at 4 Different Points (Cont’d)
• Chapter 3.1: Slope of a Curve - 16) Intro to Using Calculator
• Chapter 3.1: Slope of a Curve - 17) Calculator Tips-Slope of Tangent Line
• Chapter 3.1: Slope of a Curve - 18) Equation of Tangent Line Part I
• Chapter 3.1: Slope of a Curve - 19) Equation of Tangent Line, Part II
• Chapter 3.1: Slope of a Curve - 20) Equation of Tangent Line, Part III
• Chapter 3.1: Slope of a Curve - 21) Equation of Tangent Line, Part IV
• Chapter 3.1: Slope of a Curve - 22) Introduction to Slope of Square Root Functions
• Chapter 3.1: Slope of a Curve - 23) Finding Slopes of Square Root Functions, Part I
• Chapter 3.1: Slope of a Curve - 24) Calculator Investigation of Square Root Problem
• Chapter 3.1: Slope of a Curve - 25) Finding Slopes of Square Root Functions, Part II
• Chapter 3.1: Slope of a Curve - 26) Finding Equation of Tangent Line to Square Root Function
• Chapter 3.1: Slope of a Curve - 27) Slope of Square Root Function, Example 2
• Chapter 3.1: Slope of a Curve - 28) Slope of Square Root Function at Any x
• Chapter 3.1: Slope of a Curve - 29) Existence of Tangent Line, Part I
• Chapter 3.1: Slope of a Curve - 30) Existence of Tangent Line, Part II
• Chapter 3.1: Slope of a Curve - 31) Existence of Tangent Line, Part III
• Chapter 3.1: Slope of a Curve - 32) Slope of a Piecewise-Defined Function
• Chapter 3.1: Slope of a Curve - 33) The Derivative and its Notation, Part I
• Chapter 3.1: Slope of a Curve - 34) Derivative Notation, Part II
• Chapter 3.1: Slope of a Curve - 35) Derivative of Cubic Function, Part I
• Chapter 3.1: Slope of a Curve - 36) Derivative of Cubic Function, Part II
• Chapter 3.1: Slope of a Curve - 37) Calculator Tip for Homework Problems
• Chapter 3.2: Derivative Rules I - 01) Introduction-Derivative of xn
• Chapter 3.2: Derivative Rules I - 02) Derivatives of Linear and Constant Functions of Derivative of xn, Part I
• Chapter 3.2: Derivative Rules I - 03) Proof of Derivative of xn, Part II
• Chapter 3.2: Derivative Rules I - 04) Review of Laws of Exponents, Part I
• Chapter 3.2: Derivative Rules I - 05) Review of Laws of Exponents, Part II
• Chapter 3.2: Derivative Rules I - 06) Constant Multiplier Rule and Examples
• Chapter 3.2: Derivative Rules I - 07) The Sum Rule and Examples
• Chapter 3.2: Derivative Rules I - 08) Derivative of a Polynomial
• Chapter 3.2: Derivative Rules I - 09) Equation of Tangent Line
• Chapter 3.2: Derivative Rules I - 10) Equation Tangent Line and Error
• Chapter 3.2: Derivative Rules I - 11) Understanding Percent Error
• Chapter 3.2: Derivative Rules I - 12) Calculators Tips
• Chapter 3.3: Limits and Continuity - 01) Intro. to Limits, Part I
• Chapter 3.3: Limits and Continuity - 02) Intro. to Limits, Part II
• Chapter 3.3: Limits and Continuity - 03) Intro. to Limits, Part III
• Chapter 3.3: Limits and Continuity - 04) Intro. to Limits, Part IV
• Chapter 3.3: Limits and Continuity - 05) Intro. to Limits, Part V
• Chapter 3.3: Limits and Continuity - 06) Intro. to Limits, Part VI
• Chapter 3.3: Limits and Continuity - 07) Limit Example 1
• Chapter 3.3: Limits and Continuity - 08) Limit Example 2
• Chapter 3.3: Limits and Continuity - 09) Limit Example 3
• Chapter 3.3: Limits and Continuity - 10) Limit Practice Problem
• Chapter 3.3: Limits and Continuity - 11) Theorem 1: Limit of Constant
• Chapter 3.3: Limits and Continuity - 12) Thm 2: Limit of x
• Chapter 3.3: Limits and Continuity - 13) Thm 3: Limit of kf(x)
• Chapter 3.3: Limits and Continuity - 14) Thm 4: Limit of f(x) + g(x)
• Chapter 3.3: Limits and Continuity - 15) Thm 5: Limit of f(x)g(x)
• Chapter 3.3: Limits and Continuity - 16) Thm 6: Limit of f(x)/g(x)
• Chapter 3.3: Limits and Continuity - 17) Thm 7: Limit of [f(x)]^N
• Chapter 3.3: Limits and Continuity - 18) Limit of Square Root
• Chapter 3.3: Limits and Continuity - 19) Limits Using Theorems
• Chapter 3.3: Limits and Continuity - 20) Limit of Difference Quotient
• Chapter 3.3: Limits and Continuity - 21) Another Difference Quotient Limit
• Chapter 3.3: Limits and Continuity - 22) One-Sided Limits
• Chapter 3.3: Limits and Continuity - 23) Limits of Piecewise Defined Functions
• Chapter 3.3: Limits and Continuity - 24) Piecewise Defined with "Hole"
• Chapter 3.3: Limits and Continuity - 25) Piecewise Defined with "Jump"
• Chapter 3.3: Limits and Continuity - 26) Piecewise Limit without Graph
• Chapter 3.3: Limits and Continuity - 27) Practice with Piecewise
• Chapter 3.3: Limits and Continuity - 28) Continuity, Part I
• Chapter 3.3: Limits and Continuity - 29) Continuity, Part II
• Chapter 3.3: Limits and Continuity - 30) Continuity, Part III
• Chapter 3.3: Limits and Continuity - 31) Definition of Continuous
• Chapter 3.3: Limits and Continuity - 32) Example: "Discuss Continuity"
• Chapter 3.3: Limits and Continuity - 33) Differentiability and Continuity
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 01) Why Division by 0 is Undefined and 0/0 Indeterminate
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 02) Lim as x->0+ of 1/x
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 03) Lim as x->0- of 1/x
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 04) Lim as x->0 of 1/x
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 05) Lim as x->0 of 1/x2
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 06) Lim as x->0 of -1/x2 and Shortcut to Finding Infinite Limits
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 07) Lim as x->2 of 1/(x-2)
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 08) 4 Examples of Infinite Limits
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 09) Lim as x->a+ of 1/(x-a)n
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 10) Lim as x->a- of 1/(x-a)n and lim x->-3- of x/(x+3)
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 11) Lim as x->-3+ of x/(x+3)
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 12) Lim as x->-7-
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 13) 2 More Infinite Limits
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 14) Pond Problem 1
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 15) Pond Problem 2
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 16) Pond Problem 3
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 17) Lim as x->infinity of (100,000 + 215x) / x
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 18) Shortcuts for 2 Limits at Infinity
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 19) 3 Limits x-> Infinity
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 20) More Limits at Infinity, and Summary
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 21) Sketch Graph of Rational Function
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 22) TI-89: Finding Limits
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 23) TI-89: Finding Limits at Infinity and Infinite Limits Exactly
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 24) A Problem Similar to Homework, Part I
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 25) A Problem from Homework, Part II
• Chapter 3.4: Limits at Infinity, Infinite Limits and Asymptotes - 26) Another Homework Problem
• Chapter 3.5: Derivative Rules 2 - 01) Summary of Derivative Rules
• Chapter 3.5: Derivative Rules 2 - 02) Motivating Product Rule
• Chapter 3.5: Derivative Rules 2 - 03) Product Rule Example 1
• Chapter 3.5: Derivative Rules 2 - 04) Product Rule Example 2
• Chapter 3.5: Derivative Rules 2 - 05) Product Rule Example 3
• Chapter 3.5: Derivative Rules 2 - 06) Product Rule with Square Root
• Chapter 3.5: Derivative Rules 2 - 07) Motivating Quotient Rule
• Chapter 3.5: Derivative Rules 2 - 08) Another Quotient to Differentiate
• Chapter 3.5: Derivative Rules 2 - 09) Quotient Rule Example 1
• Chapter 3.5: Derivative Rules 2 - 10) Quotient Rule Example 2
• Chapter 3.5: Derivative Rules 2 - 11) Quotient Rule Example 3
• Chapter 3.5: Derivative Rules 2 - 12) Using TI-89 to Show Equivalent Expressions
• Chapter 3.6: The Chain Rule - 01) Review/Derivative of Composite Function
• Chapter 3.6: The Chain Rule - 02) Motivating the Chain Rule
• Chapter 3.6: The Chain Rule - 03) Chain Rule
• Chapter 3.6: The Chain Rule - 04) Chain Rule Example
• Chapter 3.6: The Chain Rule - 05) Chain Rule Example 2
• Chapter 3.6: The Chain Rule - 06) Chain Rule Example 3
• Chapter 3.6: The Chain Rule - 07) General Power Rule
• Chapter 3.6: The Chain Rule - 08) Equation of Tangent Line
• Chapter 3.6: The Chain Rule - 09) Derivative of Square Root with Chain Rule
• Chapter 3.6: The Chain Rule - 10) Product and Chain Rules Together
• Chapter 3.6: The Chain Rule - 11) Chain, then Quotient Rule
• Chapter 3.6: The Chain Rule - 12) Quotient, then Chain Rule
• Chapter 3.6: The Chain Rule - 13) Another Use for Chain Rule, Part I
• Chapter 3.6: The Chain Rule - 14) Another Use for Chain Rule, Part II
• Chapter 3.7: Marginal Funcations and Rates of Change - 01) Marginal Cost, Example 1
• Chapter 3.7: Marginal Funcations and Rates of Change - 02) Marginal Cost, Example 2
• Chapter 3.7: Marginal Funcations and Rates of Change - 03) Practice Finding Marginal Cost
• Chapter 3.7: Marginal Funcations and Rates of Change - 04) Definition of Marginals
• Chapter 3.7: Marginal Funcations and Rates of Change - 05) Intro to Derivative
• Chapter 3.7: Marginal Funcations and Rates of Change - 06) Summary of Marginal vs. Derivative
• Chapter 3.7: Marginal Funcations and Rates of Change - 07) E'(x) approximates E(x+1) - E(x)
• Chapter 3.7: Marginal Funcations and Rates of Change - 08) Practice: Change in Revenue
• Chapter 3.7: Marginal Funcations and Rates of Change - 09) Percent Error of Approximation
• Chapter 3.7: Marginal Funcations and Rates of Change - 10) Average Cost, Revenue, or Profit
• Chapter 3.7: Marginal Funcations and Rates of Change - 11) TI-89 and Average Rate of Change
• Chapter 3.7: Marginal Funcations and Rates of Change - 12) Vertical Motion, Part I
• Chapter 3.7: Marginal Funcations and Rates of Change - 13) Vertical Motion, Part II
• Chapter 3.7: Marginal Funcations and Rates of Change - 14) Vertical Motion, Part III
• Chapter 3.7: Marginal Funcations and Rates of Change - 15) Average vs. Instantaneous Velocity
• Chapter 3.7: Marginal Funcations and Rates of Change - 16) Why Derivative Gives Instant. ROC
• Chapter 3.7: Marginal Funcations and Rates of Change - 17) Problems Using ROC, Part I
• Chapter 3.7: Marginal Funcations and Rates of Change - 18) Problems Using ROC, Part II
• Chapter 3.7: Marginal Funcations and Rates of Change - 19) Practice with Instant. Vel.
• Chapter 3.8: Implicit Differentiation - 01) Intro. to Implicit Differentiation
• Chapter 3.8: Implicit Differentiation - 02) Slope of a Circle, Part I
• Chapter 3.8: Implicit Differentiation - 03) Slope of a Circle using Imp. Diff.
• Chapter 3.8: Implicit Differentiation - 04) Equation of Tangent to Circle
• Chapter 3.8: Implicit Differentiation - 05) Practice: Equation Tangent Line
• Chapter 3.8: Implicit Differentiation - 06) Imp. Diff. Example 4
• Chapter 3.8: Implicit Differentiation - 07) Imp. Diff. Example 5
• Chapter 3.8: Implicit Differentiation - 08) Imp. Diff. Example 6
• Chapter 3.8: Implicit Differentiation - 09) Imp. Diff. Example 7
• Chapter 3.8: Implicit Differentiation - 10) Imp. Diff. Example 8
• Chapter 3.8: Implicit Differentiation - 11) TI-89 and Implicit Differentiation