Chain Rule Practice Exam Solutions

Calculus 1

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Limits - The Basics — Topic Review (⏱️ < 69 min)

Study Guide (fill this in as you watch the videos!)
Limits - Overview (p. 3-6) (11:20)
Evaluating Limits - Overview (p. 7) (5:36)
Indeterminate Forms (p. 8) (2:42)
Evaluating Limits Algebraically - Piecewise Functions (p. 9) (5:26)
Evaluating Limits Algebraically - 0/0 Form (p. 10-14) (21:28)
Evaluating Infinite Limits - Number/0 Form (p. 15) (5:56)
Evaluating Infinite Limits - Knowing Graphs (p. 16-17) (5:18)
The Squeeze Theorem (p. 18) (4:42)
Limits of Trig Functions (p. 19-20) (6:33)

Limits - The Basics — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Evaluating Limits from a Graph Practice Exam Solutions (4:30)
Evaluating Limits Algebraically Practice Exam Solutions (27:51)
The Squeeze Theorem Practice Exam Solutions (9:12)
Limits of Trig Functions Practice Exam Solutions (9:04)

Applications of Limits — Topic Review (⏱️ < 67 min)

Study Guide (fill this in as you watch the videos!)
Continuity (p. 3-4) (10:57)
Discontinuity (p. 5-8) (21:22)
The Intermediate Value Theorem (p. 9-10) (11:37)
Limits at Infinity and Horiztonal Asymptotes (p. 11-17) (23:09)

Applications of Limits — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Continuity Practice Exam Video Solutions (19:24)
The Intermediate Value Theorem Practice Exam Solutions (11:09)
Limits at Infinity Practice Exam Solutions (18:38)

Definition of the Derivative & Differentiability — Topic Review (⏱️ < 55 min)

Study Guide (fill this in as you watch the videos!)
The Definition of the Derivative (p. 3-5) (21:39)
The Derivative as a Function (p. 6-7) (8:49)
Higher-Order Derivatives (p. 8-9) (6:16)
Differentiability (p. 10-11) (10:55)
The Graph of the Derivative (p. 12-13) (7:05)

Definition of the Derivative & Differentiability — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
The Definition of the Derivative Practice Exam Solutions (16:38)
The Derivative as a Function Practice Exam Solutions (14:15)
Differentiability Practice Exam Solutions (16:46)
The Graph of the Derivative Practice Exam Solutions (10:45)

Derivative Rules — Topic Review (⏱️ < 65 min)

Study Guide (fill this in as you watch the videos!)
Derivative Rules - Overview (p. 3-4) (7:52)
Derivatives of Polynomials and Exponents (p. 5) (11:44)
Product and Quotient Rules (p. 6-7) (12:35)
Finding Tangent and Normal Lines (p. 8-9) (7:31)
Horizontal and Vertical Tangent Lines (p. 10) (3:26)
Derivatives of Trig Functions (p. 11-12) (8:25)
The Chain Rule (p. 13-14) (12:27)

Derivative Rules — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Derivative Rules Practice Exam Solutions (6:05)
Product and Quotient Rules Practice Exam Solutions (19:27)
Chain Rule Practice Exam Solutions (10:14)
Differentiation Mixed Practice Practice Exam Solutions (18:50)

Implicit Differentiation and Rates of Change Applications — Topic Review (⏱️ < 97 min)

Study Guide (fill this in as you watch the videos!)
Implicit Differentiation (p. 3-5) (17:22)
Logarithmic Differentiation (p. 6-8) (13:02)
Derivatives of Inverse Functions (p. 9) (6:48)
Derivatives of Inverse Trig Functions (p. 10-11) (8:34)
Rates of Change Applications - Motion of Particles (p. 12-14) (17:04)
Rates of Change Applications - Economics (p. 15) (9:20)
Rates of Change Applications - Chem and Bio (p. 16-17) (5:21)
Exponential Growth and Decay (p. 18-20) (16:05)
Compound Interest (p. 21) (3:34)

Implicit Differentiation and Rates of Change Applications — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Implicit Differentiation Practice Exam Solutions (12:34)
Logarithmic Differentiation Practice Exam Solutions (14:11)
Derivatives of Inverse Functions Practice Exam Solutions (8:01)
Derivatives of Inverse Trig Functions Practice Exam Solutions (7:56)
Rate of Change Applications Practice Exam Solutions (21:27)

Related Rates, Linear Approximations, and Differentials — Topic Review (⏱️ < 56 min)

Study Guide (fill this in as you watch the videos!)
Related Rates - Overview (p. 3-4) (8:11)
Related Rates - Harder Solved Examples (p. 5-7) (21:05)
Linear Approximations and Differentials (p. 8-9) (14:25)
Differentials and Error Measurement (p. 10-12) (12:13)

Related Rates, Linear Approximations, and Differentials — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Related Rates Practice Exam Solutions (21:59)
Linear Approximations Practice Exam Solutions (11:36)
Differentials Practice Exam Solutions (5:25)

Hyperbolic Functions — Topic Review (⏱️ < 6 min)

Study Guide (fill this in as you watch the videos!)
Hyperbolic Functions (p. 3-4) (5:16)

Hyperbolic Functions — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Hyperbolic Functions Practice Exam Solutions (6:50)

Maxima and Minima, Curve Sketching, and The Mean Value Theorem — Topic Review (⏱️ < 87 min)

Study Guide (fill this in as you watch the videos!)
Maximum and Minimum Values - Overview (p. 3) (5:52)
Critical Numbers and the First Derivative Test (p. 4-7) (20:21)
Finding Absolute Extrema (p. 8-9) (9:21)
Inflection Points and Concavity (p. 10-11) (10:26)
The Second Derivative Test (for Local Extrema) (p. 12-13) (6:16)
Graphing (p. 14-17) (22:47)
Rolle’s Theorem and The Mean Value Theorem (p. 18-20) (11:48)

Maxima and Minima, Curve Sketching, and The Mean Value Theorem — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Critical Numbers and Increasing/Decreasing Behavior Practice Exam Solutions (8:22)
Absolute Extrema Practice Exam Solutions (9:45)
Relative Extrema with The First Derivative Test Practice Exam Solutions (15:56)
Concavity Practice Exam Solutions (8:48)
The Second Derivative Test Practice Exam Solutions (8:16)
Graphing Practice Exam Solutions (15:51)
Rolle's Theorem and The Mean Value Theorem Practice Exam Solutions (8:13)

Optimization — Topic Review (⏱️ < 21 min)

Study Guide (fill this in as you watch the videos!)
Optimization (p. 3-5) (20:24)

Optimization — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Optimization Practice Exam Solutions (70:49)

L'Hôpital's Rule — Topic Review (⏱️ < 25 min)

Study Guide (fill this in as you watch the videos!)
Indeterminate Forms and L'Hôpital's Rule (p. 3-5) (15:02)
Growth Rates (How to Skip L'Hôpital's Rule) (p. 6) (4:51)
How to Do Nasty Limits and Skip the Algebra 😈 (p. 7) (4:10)

L'Hôpital's Rule — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
L'Hôpital's Rule Practice Exam Solutions (24:01)

Antiderivatives and Indefinite Integrals, Initial Value Problems, and Motion — Topic Review (⏱️ < 37 min)

Study Guide (fill this in as you watch the videos!)
Antiderivatives and Indefinite Integrals (p. 3-6) (13:38)
Initial Value Problems (p. 7-9) (8:40)
Physics Applications - Motion of a Particle (p. 10) (4:22)
Distance vs. Displacement (p. 11) (10:14)

Antiderivatives and Indefinite Integrals, Initial Value Problems, and Motion — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Basic Antiderivatives/Indefinite Integrals Practice Exam Solutions (2:55)
Harder Antiderivatives/Indefinite Integrals Practice Exam Solutions (5:34)
Initial Value Problems Practice Exam Solutions (2:18)
Motion Problems Practice Exam Solutions (17:35)

Newton's Method — Topic Review (⏱️ < 19 min)

Study Guide (fill this in as you watch the videos!)
Newton's Method (p. 3-5) (18:47)

Newton's Method — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Newton's Method Practice Exam Solutions (11:49)

Definite Integrals, Area, and Average Value of a Function — Topic Review (⏱️ < 99 min)

Study Guide (fill this in as you watch the videos!)
Approximating Area Under the Curve (p. 3-6) (15:59)
The Definite Integral (p. 7-10) (17:09)
Evaluating Definite Integrals of Even and Odd Functions (p. 11-12) (9:26)
Evaluating Definite Integrals Using Geometry (p. 13-15) (11:07)
Comparison Property (p. 16-17) (10:10)
Finding the Definite Integral Using Limits (p. 18-21) (29:22)
The Average Value of a Function (p. 22) (6:01)

Definite Integrals, Area, and Average Value of a Function — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Approximating Area Under the Curve Practice Exam Solutions (7:46)
Properties of Definite Integrals Practice Exam Solutions (7:37)
Evaluating Definite Integrals Using Geometry Practice Exam Solutions (4:35)
Finding the Definite Integral Using Limits Practice Exam Solutions (7:47)
The Average Value of a Function Practice Exam Solutions (4:51)

Fundamental Theorem of Calculus and Applications — Topic Review (⏱️ < 31 min)

Study Guide (fill this in as you watch the videos!)
The Fundamental Theorem of Calculus (p. 3-4) (6:00)
Fundamental Theorem of Calculus with Chain Rule (p. 5-6) (7:02)
The Net Change Theorem (p. 7-8) (4:48)
Applications to Particle Motion - Distance vs Displacement (p. 9-10) (13:21)

Fundamental Theorem of Calculus and Applications — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
The Fundamental Theorem of Calculus Practice Exam Solutions (4:37)
The Fundamental Theorem of Calculus with Chain Rule Practice Exam Solutions (11:03)
The Net Change Theorem Practice Exam Solutions (8:28)

Substitution — Topic Review (⏱️ < 44 min)

Study Guide (fill this in as you watch the videos!)
Substitution (p. 3-6) (16:26)
My F***ing Variable Didn't Cancel (p. 7) (4:23)
Substitution with Definite Integrals (p. 8-10) (11:52)
Substitution vs Basic Integration (p. 11-12) (10:54)

Substitution — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Substitution Practice Exam Solutions (18:12)
Substitution with Definite Integrals Practice Exam Solutions (11:19)
Mixed Integration Practice (Substitution vs Basic Integral Rules) Practice Exam Solutions (16:55)

Area Between Curves & Volume of Solids of Revolution — Topic Review (⏱️ < 72 min)

Study Guide (fill this in as you watch the videos!)
Area Between Curves (p. 3-4) (9:58)
Volume by Cross Sectional Area (p. 5-6) (11:16)
Solids of Revolution - Disk and Washer Method (p. 7-10) (14:34)
Solids of Revolution - Shell Method (p. 11-12) (8:00)
Rotating About Other Axes (p. 13-14) (13:51)
Which One - Disk or Shell? (p. 15-17) (14:21)

Area Between Curves & Volume of Solids of Revolution — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Areas Between Curves Practice Exam Solutions (14:41)
Volume by Cross Sectional Area Practice Exam Solutions (11:16)
Disk/Washer Method Practice Exam Solutions (36:25)
Shell Method Practice Exam Solutions (35:35)

Parametric Equations — Topic Review (⏱️ < 72 min)

Study Guide (fill this in as you watch the videos!)
Plane Curves & Parametric Equations (p. 3-5) (19:52)

Parametric Equations — Practice Exam Questions

Practice Exam Questions
Practice Exam Answer Key
Plane Curves & Parametric Equations Practice Exam Solutions (19:09)

[OPTIONAL] Sh*t You Forgot from Precalc

Study Guide (fill this in as you watch the videos!)
Special Products and Factoring (p. 3-6) (19:55)
Ways to Represent a Function (p. 7-8) (7:49)
Finding the Domain of a Function (p. 9) (4:31)
Piecewise Functions (p. 10) (9:29)
Even vs Odd vs Neither (p. 11-12) (6:02)
Increasing, Decreasing, Constant (p. 13) (2:57)
Essential Functions (p. 14-19) (15:15)
Transforming Functions (p. 20-22) (12:22)
Combinations of Functions (p. 23) (4:11)
Composite Functions (p. 24) (6:26)
Exponential Functions (p. 25) (5:01)
Inverse Functions (p. 26-28) (11:28)
Logarithms (p. 29-31) (9:58)
Exponents and Logs - Side by Side (p. 32-36) (11:19)
Linear Functions (p. 37-39) (10:20)
Solving Inequalities (p. 40-41) (10:50)
Rational Functions (p. 42-45) (16:34)

[OPTIONAL] Sh*t You Forgot from Trig

Study Guide (fill this in as you watch the videos!)
Trig Functions (p. 3) (4:25)
The Unit Circle (p. 4-7) (17:35)
Trig Identities (p. 8-9) (7:39)
Solving Trig Equations and Inequalities (p. 10-11) (16:13)
Inverse Trig Overview (p. 12-13) (7:46)
Evaluating Mixed Trig Function Expressions (p. 14-17) (10:47)
Evaluating Mixed Trig Function Expressions with Variables (p. 18) (3:50)

Chain Rule Practice Exam Solutions

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