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John Zhu

John Zhu

Power Rule

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Table of Contents

Section 1: Functions
Definitions & Properties of Functions

11m 26s

Intro
0:00
Definition
0:28
Properties: Vertical Line Test
1:32
Domain
1:38
Range
1:59
Vertical Line test
2:19
Example 1
2:33
Example 2
3:10
Properties: Roots or Zeros
4:04
Finding the Root
4:16
Properties: Forms
5:12
Graphically
5:20
List
5:46
Equation
6:11
Function
6:38
Properties: Odd & Even
7:12
Even Function
7:14
Odd Function
8:25
Properties: Increasing & Decreasing
9:17
Increasing Function
9:22
Decreasing Function
10:21
Graphing

13m 58s

Intro
0:00
Manipulating
0:10
A in the Equation
0:39
B in the Equation
0:44
C & D in the Equation
0:49
Negative values
0:59
Example 1
1:17
Example 2
1:51
Example 3: Absolute Value Functions
3:43
Example 4
4:57
Example 5
6:17
Example 6
8:02
Example 7
9:10
Example 8
11:02
Example 9
11:47
Inverse Functions

6m 47s

Intro
0:00
Inverse
0:08
Definition
0:18
Example: Finding the Inverse
1:03
Example 2
2:29
Example 3
3:12
Example 4
4:41
Polynomial Functions

5m 4s

Intro
0:00
Types of Functions: Polynomials
0:07
No Domain Restrictions
0:12
No Discontinuities
0:19
Degree Test
0:31
Types of Functions: Polynomials
1:17
Leading Coefficient Test
1:33
Leading Coefficient Positive, Even Degree
1:54
Leading Coefficient Positive, Odd Degree
2:13
Leading Coefficient Negative Even Degree
2:34
Leading Coefficient Positive, Odd Degree
2:46
Examples: Types of Functions: Polynomials
3:03
Examples: Types of Functions: Polynomials
4:18
Trigonometric Functions

6m 45s

Intro
0:00
Types of Functions: Trigonometric
0:05
6 Functions To Be Familiar With
0:14
Example 1: SIN
1:38
Example 2: COS
3:22
Example 3: TAN
4:38
Inverse Trigonometric Functions

5m 58s

Intro
0:00
Types of Functions: Trigonometric- Inverse Trig Functions
0:07
Example: Inverse SIN of X
0:45
Example: Inverse Function
2:30
Example: Inverse TAN of X
4:42
Trigonometric Identities

17m 42s

Intro
0:00
Types of Functions: Trigonometric- Trig Identities
0:07
4 Identities
0:24
Pythagorean
0:28
Double Angle
1:10
Power Reducing
1:28
Sum or Difference
1:42
Couple More Identities
1:59
Negative Angle
2:04
Product to Sum
2:39
Example 1: Prove
3:00
Example 2: Simplify Expression
5:02
Example 3: Prove
5:56
Example 4: Prove
8:02
Example 5: Prove With TAN
12:43
Exponential Functions

5m 53s

Intro
0:00
Types of Functions: Exponentials
0:07
General Form
0:10
Special Exponential Function
0:17
Example 1: Using Exponential Properties
0:46
Example 2: Using Exponential Properties
1:58
Example 3: Using Trig Identities & Exponential Properties
3:16
Example 4: Using Exponential Properties
4:37
Logarithmic Functions

7m 8s

Intro
0:00
Types of Functions: Logarithmic
0:06
General Form
0:10
2 Special Logarithmic Func.
0:19
Euler's # / Natural Log
0:27
Logarithmic & Exponential Relationship
0:45
Log form
1:56
Properties
2:09
Example 1: Apply Basic Principle of Log Func.
3:05
Example 2: Use Properties
3:40
Example 3: Regular Log
5:16
Rational Functions

15m 36s

Intro
0:00
Types of Functions: Rational - Definition
0:06
Example 1: Graph Rational Func.
0:36
Example 2: Find Asymptotes of Func.
7:02
Example 3: Find Asymptotes of Func.
8:59
Example 4: Graph Rational Func.
11:08
Conic Sections

14m 58s

Intro
0:00
Types of Conic Sections
0:06
Parabolas
0:19
Circles
1:36
Ellipses
2:40
Hyperbolas
4:42
Complete the Square
6:40
Example: Conic Sections
9:08
Example 2: Conic Sections
10:59
Example 3: Graph Conic Sections
12:21
Section 2: Limits and Continuity
Limit Definition & Properties

7m 15s

Intro
0:00
Definition
0:06
Example: Limit
0:17
Properties
1:13
1st Property
1:21
2nd Property
1:34
Special Property
1:51
Limits
2:36
Explain Example
2:49
Limits Example
4:39
Limits Example
5:21
Solving Limits with Algebra

8m 1s

Intro
0:00
Solving Limits with Algebra
0:07
Example 1: Solve Algebraically
0:30
Solving Limits with Algebra, Example 2
2:28
Solving Limits with Algebra, Example 3
3:18
Solving Limits with Algebra, Example 4
4:56
Solving Limits with Algebra, Example 5
6:26
Rational Limit Rules

3m 16s

Intro
0:00
Rational Limit Rules
0:07
Review of Solving Problem Algebraically
0:08
Limit Rules
0:28
Rule 1
0:35
Rule 2
0:40
Rule 3
0:45
Rational Limit Rules
1:02
Applying 1st Rule
1:22
Rational Limit Rules
1:50
Applying 2nd Rule
2:09
Rational Limit Rules
2:26
Applying 3rd Rule
2:40
One Sided Limits

9m 57s

Intro
0:00
Types of Limits: One-Sided Limit Rules
0:06
Example
0:19
Applying Same Rule
0:34
Rule to Keep In Mind
0:52
Types of Limits: One-Sided Limit Example 1
1:12
Limit of x² From Negative Side
2:11
Types of Limits: One-Sided Limit, Example 2
2:27
Types of Limits: One-Sided Limit, Example 3
4:26
Types of Limits: One-Sided Limit, Example 4
5:47
One-Sided Limit Example: X with Even Degree Polynomial
7:00
One-Sided Limit Example: Entire Denominator Squared
8:09
Special Trigonometric Limits

8m 28s

Intro
0:00
Types of Limits: Special Trig Limits
0:07
Pre-set Rules
0:35
Special Trig Limits, Example 1
0:58
Special Trig Limits, Example 2
2:50
Special Trig Limits, Example 3
3:55
Special Trig Limits, Example 4: With More Degrees
4:57
Special Trig Limits, Example 5
6:21
Limits & Continuity

10m 14s

Intro
0:00
Definition
0:06
3 Rules: f(x) Is Continuous…
0:21
Example 1: Finding Continuity
1:06
Types of Discontinuity
2:44
Jump
2:52
Point
3:24
Essential (Asymptote)
3:47
Removable
4:17
Example 2: Continuity Examples
4:41
Example 3: Continuity Examples
6:13
Example 4: Locate & Identify Type of Discontinuities
8:00
Limits: Multiple Choice Practice

6m 16s

Intro
0:00
Problem 1
0:08
Problem 2
1:51
Problem 3
2:54
Problem 4
4:31
Section 3: Derivatives
Derivative Definition & Properties

4m 11s

Intro
0:00
Definition
0:09
Formal Definition
0:45
Difference Quotient
1:12
Basic Derivatives
1:16
Differentiability
2:54
Basic Rules of Differentiation

7m 7s

Intro
0:00
Basic Rules of Differentiation
0:09
Constant Rule
0:14
Constant Multiple Rule
1:10
Addition and Difference Rule
1:40
Example 1: Constant Rule
2:25
Example 2: Constant Multiple Rule
3:01
Example 3: Constant Multiple Rule
3:35
Example 4: Constant Rule
4:34
Example 5: Constant Multiple Rule
5:03
Example 6
5:33
Power Rule

7m 14s

Intro
0:00
Power Rule
0:07
Power Rule Definition
0:30
Example 1
1:11
Example 2
2:25
Example 3
3:05
Example 4
4:18
Example 5
5:13
Trigonometric Rules

7m 53s

Intro
0:00
Trigonometric Rules
0:07
COS X
0:38
Find Derivative
1:02
Example 1
2:46
Example 2: COS Function
3:09
Example 3: Composite Expression
3:54
Example 4: Sec Function
5:02
Example 5: CSC
5:33
Example 6L COT
6:42
Product Rule

11m 11s

Intro
0:00
Product Rule
0:07
Definition
0:20
Example 1
0:43
Example 2
2:11
Example 3
4:24
Example 4
5:24
Example 5
6:42
Example 6
7:51
Quotient Rule

16m 50s

Intro
0:00
Quotient Rule
0:07
Definition
0:30
Example 1
1:17
Example 2: With No X In Numerator
2:49
Example 3
4:30
Example 4: With Decimals
6:46
Example 5
8:53
Example 6: With Trig Functions
12:55
Chain Rule

19m 48s

Intro
0:00
Chain Rule
0:07
Definition
0:17
Example 1: Applying the Chain Rule
1:33
Example 2
4:25
Example 3
6:02
Example 4
9:25
Example 5
12:47
Example 6
15:27
Higher Order Derivatives

15m

Intro
0:00
Types of Derivatives: Higher Order Derivatives
0:07
1st Derivative / F Prime
0:19
2nd Derivative
0:25
3rd Derivative
0:32
Example 1
1:48
Example 2: Find 3rd Derivative
3:13
Example 3: Acceleration
4:25
Example 4
10:20
Example 5: 2nd Derivative
12:11
Derivatives of Exponential Functions

13m 14s

Intro
0:00
Types of Derivatives: Exponential Functions
0:08
Derivatives: Definition/ Formula
0:28
Example 1
1:25
Example 2
2:47
Example 3
4:13
Example 4
7:11
Example 5
9:23
Example 6
11:06
Derivatives of Logarithmic Functions

11m 30s

Intro
0:00
Types of Derivatives: Logarithmic Functions
0:06
Rule for Logarithmic Functions
0:28
Example 1
0:58
Example 2
3:10
Example 3
4:38
Example 4
7:18
Example 5
8:48
Example 6
9:38
Derivatives of Inverse Trigonometric Functions

16m 54s

Intro
0:00
Types of Derivatives: Inverse Trigonometric Functions
0:06
6 Fundamental Properties of Inverse Trigonometric Functions
0:38
Example 1
2:17
Example 2
3:41
Example 3
5:37
Example 4
7:24
Example 5
10:08
Implicit Differentiation

16m 53s

Intro
0:00
Implicit Differentiation: First Order
0:07
Example 1: Setting Up
0:45
Example 1: Solving
1:41
Implicit Differentiation: Second Order (Ex. 2)
4:55
Example 3: Implicit Differentiation
9:11
Example 4: Implicit Differentiation
9:56
Example 5: Implicit Differentiation With Double Derivative
12:46
Multiple Choice Practice: Derivatives

11m 7s

Intro
0:00
Practice Problem 1
0:09
Answer
3:24
Practice Problem 2
3:36
Answer
6:29
Practice Problem 3
6:42
Answer
8:39
Practice Problem 4
8:43
Answer
9:33
Practice Problem 5
9:41
Answer
10:40
Section 4: Applications of Derivatives
Tangent & Normal Lines

22m 36s

Intro
0:00
Tangent and Normal Lines
0:10
Definition
0:22
Example 1
0:55
Tangent and Normal Lines: Example 2
2:43
Tangent and Normal Lines
5:21
Example 3
5:35
Tangent and Normal Lines: Example 4
9:14
Tangent and Normal Lines: Example 5
12:27
Tangent and Normal Lines: Example 6
15:54
Tangent and Normal Lines: Example 7
19:05
Position Velocity & Acceleration

18m 42s

Intro
0:00
Position, Velocity, and Acceleration
0:10
Position Function
0:14
Velocity Function
0:34
Acceleration Function
1:01
Example 1
1:20
Example 2
6:31
Example Continue: Velocity When Acceleration is Zero
6:32
Example 3: Where Is Particle Changing Directions?
8:16
Example 4: Total Distance Traveled From 0 to 2 Second
11:09
Example 5: Ball Drop Problem
16:40
Related Rates

26m 22s

Intro
0:00
Related Rates
0:06
Finding Rate of Change: Organization & Big Picture
0:23
Example 2: Area of a Circle
1:17
Example 3: Spherical Volume Expanding
4:19
Example 4: Traveling Problem
7:57
Example 5: Square Increase
12:37
Example 6: Standard Related Rates Problem
16:59
Example 7: Standard Related Rates Problem
19:49
Minimum & Maximum

12m 22s

Intro
0:00
Extrema: First Derivative Test
0:09
Example 1
0:46
Example 2: Real World Application/ Cost Function
4:05
Example 3: Minimums & Maximums
7:10
Example 4: Find Critical Points
10:52
Concavity

11m 43s

Intro
0:00
Concavity: Second Derivative Test
0:06
Definition
0:34
Example 1
0:54
Example 2
2:51
Example 3
4:08
Example 4
5:52
Rolles Theorem

8m 28s

Intro
0:00
Rolle's Theorem
0:07
Conditions
0:11
Summary
0:41
Example 1
1:09
Example 2
3:08
Example 3
4:48
Mean Value Theorem

9m 39s

Intro
0:00
Mean Value Theorem
0:06
Rolle's Theorem
0:07
Mean Value Theorem Conditions
0:24
Mean Value Theorem Definition
0:36
Example 1
0:56
Example 2
2:44
Example 3
5:28
Example 4
7:15
Differentials

12m 25s

Intro
0:00
Differentials
0:08
1st Differential Formula
0:29
2nd Differential Formula
0:57
Example 1
1:06
Example 2
3:21
Example 3
5:49
Example 4
7:19
Example 5
9:06
Applications of Derivatives: Multiple Choice Practice

13m 21s

Intro
0:00
Practice Problem 1
0:10
Answer
1:57
Practice Problem 2
2:08
Answer
5:39
Practice Problem 3
5:45
Answer
9:59
Practice Problem 4
10:12
Answer
11:49
Practice Problem 5
11:52
Answer
13:00
Applications of Derivatives: Free Response Practice

10m 22s

Intro
0:00
Practice Problem 1
0:10
Slope
1:30
Tangent Line Equation
2:17
Absolute Minimum
2:24
2 Possible X Points With Minimums
3:15
One Interest Point
4:14
Concavity
4:33
Positive Value = Positive Concavity
4:10
Minimum Point
5:34
Absolute Minimum
6:18
Point(s) of Inflection
6:31
Definition
6:49
2 Points Of Inflection
9:59
Section 5: Integrals
Definition of Integrals

1m 8s

Intro
0:00
Definition
0:09
Definition
0:16
Example
0:20
Integrals of Power Rule

8m 50s

Intro
0:00
Power Rule
0:06
Example 1
0:25
Example 2
2:02
Example 3
2:54
Example 4
3:45
Example 5
4:49
Example 6
6:47
Integrals Basic Rules of Integration

9m 43s

Intro
0:00
Basic Rules of Integration
0:09
Constant Rule
0:22
Example 1
0:40
Addition and Difference Rule
1:40
Example 2
1:58
Example 3: Subtraction/ Difference Rule
2:47
Example 4
3:55
Example 5
5:19
Example 6
7:37
Trigonometric Rules of Integrals

8m 58s

Intro
0:00
Trigonometric Rules
0:09
Integral of SIN
0:38
Example 1: Integral of SIN
1:46
Example 2: Integral of COS
2:38
Example 3: With 2 terms of X
3:06
Example 4: Integral of SEC
4:15
Example 5: Integral of CSC
5:06
Example 6
6:18
Chain Rule

13m 59s

Intro
0:00
Chain Rule
0:07
Example 1
0:37
Example 2
3:17
Example 3
5:09
Example 4
7:53
Example 5
9:40
Example 6
11:39
Integrals of Exponential Functions

12m 52s

Intro
0:00
Types of Integrals: Exponential Functions
0:09
Rule 1
0:30
Rule 2
0:49
Example 1
1:11
Example 2
2:54
Example 3
4:19
Example 4
5:19
Example 5
7:37
Example 6
9:04
Integrals of Natural Logarithmic Functions

13m

Intro
0:00
Types of Integrals: Natural Log Functions
0:09
Example 1
0:49
Example 2
2:06
Example 3
4:01
Example 4
5:37
Example 5
7:30
Example 6
9:05
Integrals of Inverse Trigonometric Functions

8m 29s

Intro
0:00
Types of Integrals: Inverse Trig Functions
0:09
One Property
0:40
Example 1
1:19
Example 2
3:44
Example 3
4:53
Example 4
5:53
Integrals: Multiple Choice Practice

15m 37s

Intro
0:00
Problem 1
0:09
Answer
4:09
Problem 2
4:33
Answer
5:54
Problem 3
5:59
Answer
8:02
Problem 4
8:06
Answer
10:27
Problem 5
10:43
Answer
14:46
Section 6: Applications of Integrals
Fundamental Theorem of Calculus

15m 55s

Intro
0:00
Fundamental Theorem of Calculus: Properties
0:10
Definition of Integral
0:49
Example 1
1:14
Fundamental Theorem of Calculus: Properties
2:40
Rule 1
2:50
Rule 2
3:14
Rule 3
3:33
Rule 4
3:52
Example 2
4:07
Example 3
6:17
Example 4
9:31
Example 5
10:52
Example 6
13:34
Area Under A Curve

18m 34s

Intro
0:00
Area Under Curve
0:07
Definition of Integral
0:09
Left Endpoint
1:17
Right Endpoint
1:47
Midpoints
2:09
Example 1
2:40
Example 2
4:59
Example 3
8:48
Example 4
10:23
Example 5
12:30
Example 6
15:32
Reimann Sums

10m 35s

Intro
0:00
Reimann Sums
0:08
Definition
1:07
Example 1
2:48
Example 2
5:38
Example 3
7:21
Example 4
9:14
Trapezoid Rule

12m 46s

Intro
0:00
The Trapezoid Rule
0:09
Definition: Area Of A Trapezoid
0:26
Terms of Formula
1:35
Example 1
2:11
Example 2
4:29
Example 3
7:22
Example 4
10:01
Mean Value Theorem

11m 22s

Intro
0:00
Mean Value Theorem of Integration
0:06
Example 1
0:53
Example 2
2:29
Example 3
3:48
Example 4
6:02
Second Fundamental Theorem of Calculus

4m 44s

Intro
0:00
Second Fundamental Theorem of Calculus
0:07
Definition
0:39
Example 1
1:08
Example 2
2:07
Example 3
2:48
Example 4
3:23
Area Between Curves

16m 39s

Intro
0:00
Example 1
0:10
Example 2
3:00
Example 3
4:46
Example 4
8:22
Example 5
11:04
Example 6
13:09
Revolving Solids Washer Disk Methods

21m 9s

Intro
0:00
Revolving Solids Washer Disk Methods
0:11
Explanation
0:33
Formula
3:12
Example 1
3:42
Example 2
6:54
Example 3
9:29
Example 4
12:16
Example 5
15:35
Revolving Solids Cylindrical Shells Method

26m 46s

Intro
0:00
Revolving Solids: Cylindrical Shells Method
0:09
Volume Of A Solid
0:25
Formula
2:51
Example 1
2:56
Example 2
7:28
Example 3
11:39
Example 4
17:36
Example 5
21:45
Revolving Solids Known Cross Sections

27m 41s

Intro
0:00
Revolving Solids Known Cross Sections
0:08
Example 1
0:35
Example 2
6:01
Example 3
11:03
Example 4
17:29
Example 5
22:19
Differential Equations Eulers Method

17m 54s

Intro
0:00
Differential Equations
0:08
Example 1
0:30
Differential Equations: Euler's Method
2:33
Rules
2:39
Example 2
3:00
Example 3
5:42
Example 4
9:44
Example 5
14:14
Differential Equations Slope Fields

16m 30s

Intro
0:00
Slope Fields
0:08
What Are Slope Fields
0:21
Example 1
0:42
Example 2
6:30
Example 3
11:17
Application of Integrals: Multiple Choice Practice

14m 19s

Intro
0:00
Practice Problem 1
0:10
Answer
3:46
Practice Problem 2
3:49
Answer
6:20
Practice Problem 3
6:26
Answer
8:02
Practice Problem 4
8:07
Answer
10:58
Practice Problem 5
11:05
Answer
14:06
Application of Integrals: Free Response Practice

9m 14s

Intro
0:00
Problem 1
0:10
Part A
0:24
Part A: Solution
2:04
Part B
2:10
Problem 1, Part B Continue
2:23
Part B: Solution
6:15
Problem 1, Part C
6:58
Part C: Solution
12:40
Problem 2
12:52
Part A
13:02
Part A: Solution
15:34
Part B
16:03
Part B: Solution
18:48
Section 7: Sample AP Test
AP Calculus AB Practice test: Section 1: Multiple Choice Part 1

17m 50s

Intro
0:00
Problem 1
0:20
Problem 2
1:24
Problem 3
2:53
Problem 4
3:56
Problem 5
8:18
Problem 6
9:06
Problem 7
10:14
Problem 8
12:16
Problem 9
14:13
AP Calculus AB Practice test: Section 1: Multiple Choice Part 2

17m 32s

Intro
0:00
Problem 10
0:18
Problem 11
2:26
Problem 12
6:11
Problem 13
7:04
Problem 14
8:06
Problem 15
10:32
Problem 16
11:40
Problem 17
13:00
Problem 18
14:43
AP Calculus AB Practice test: Section 1: Multiple Choice Part 3

22m 14s

Intro
0:00
Problem 19
0:21
Problem 20
2:33
Problem 21
7:23
Problem 22
10:24
Problem 23
12:18
Problem 24
13:13
Problem 25
15:52
Problem 26
17:03
Problem 27
19:44
AP Calculus AB Practice test: Section 1: Multiple Choice Part 4

19m 35s

Intro
0:00
Problem 28
0:23
Problem 29
3:50
Problem 30
5:31
Problem 31
9:02
Problem 32
10:07
Problem 33
11:27
Problem 34
13:47
Problem 35
15:21
Problem 36
16:53
AP Calculus AB Practice test: Section 1: Multiple Choice Part 5

25m 43s

Intro
0:00
Problem 37
0:22
Problem 38
2:27
Problem 39
5:36
Problem 40
7:21
Problem 41
10:08
Problem 42
11:29
Problem 43
13:07
Problem 44
18:18
Problem 45
21:08
AP Calculus AB Practice Test: Section 2: Free Response Part 1

16m 50s

Intro
0:00
Problem 1, Part A
0:20
Problem 1, Part B
3:03
Problem 1, Part C
4:11
Problem 1, Part D
5:36
Problem 2, Part A
7:37
Problem 2, Part B
9:02
Problem 2, Part C
12:31
AP Calculus AB Practice Test: Section 2: Free Response Part 2

21m 36s

Intro
0:00
Problem 3, Part A
0:18
Problem 3, Part B
5:57
Problem 4, Part A
11:26
Problem 4, Part B
12:28
Problem 4, Part C
15:35
Problem 4, Part D
18:56
AP Calculus AB Practice Test: Section 2: Free Response Part 3

13m 39s

Intro
0:00
Problem 5, Part A
0:21
Problem 5, Part B
3:07
Problem 5, Part C
6:43
Problem 6
8:24
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Lecture Comments (3)

0 answers

Post by Salman Sarwar on September 28, 2014

There is a practice question that asks "Find the derivative of y = x^[1/3]"
The answer is listed as being "[1/3]x^−[1/3]" however the correct answer is [1/3]x^−[2/3].

Just wanted to clarify for anyone doing the practice questions.

1 answer

Last reply by: Manoj Sharma
Wed Aug 20, 2014 2:08 PM

Post by Manoj Sharma on August 20, 2014

Hey guys I was wondering on Example 3, If n should actually be -1. Since n-1= -2, then you would add 1 both sides and get the answer of -1. Please let me know if I am wrong.

Power Rule

  • Power rule:
  • To avoid confusion, treat n as just a constant
  • Misleading constants: natural logs, fractions, and decimals

Power Rule

Find the derivative of y = 2x3 + 5x2 + 7x + 11
  • dy = [d/dx] (2x3 + 5x2 + 7x + 11)
  • = 2[d/dx] x3 + 5 [d/dx] x2 + 7 [d/dx] x
  • = 2(3x2) + 5(2x) + 7(1) =
6x2 + 10x + 7
Find the derivative of y = x[1/3]
  • dy = [d/dx] x[1/3]
[1/3] x−[1/3]
Find the derivative of y = (x + 4)2
  • dy = [d/dx] (x + 4)2
  • = [d/dx] (x2 + 8x + 16)=
2x + 8
Find the derivative of y = √2 x2
  • dy = [d/dx] √2 x2
  • = √2 [d/dx] x2 =
2 √2 x
Find the derivative of y = 2 √x
  • dy = [d/dx]2 √x
  • = 2 [d/dx] √x
  • = 2 [d/dx] x[1/2]
  • = 2 [1/2] x−[1/2]
  • = x−[1/2] =
[1/(√x)]
Find the derivative of y = [(x3)/(x[1/3])]
  • dy = [d/dx] [(x3)/(x[1/3])]
  • = [d/dx] x3 x−[1/3]
  • = [d/dx] x(3 − [1/3])
  • = [d/dx] x[8/3]
[8/3] x[5/3]
Find the derivative of y = (√x + 1)2
  • dy = [d/dx] (√x + 1)2
  • = [d/dx] (x + 2√x + 1)
= 1 + x−[1/2]
Find the derivative of y = x − [(x3)/3!] + [(x5)/5!]
  • dy = [d/dx] (x − [(x3)/3!] + [(x5)/5!])
  • = 1 − [(3x2)/3!] + [(5x4)/5!]
1 − [(x2)/2!] + [(x4)/4!]
NOTE: y in this problem is a truncated version of the series representation of sin(x).
Find the derivative of y = 1 − [(x2)/2!] + [(x4)/4!] − [(x6)/6!]
  • dy = [d/dx] (1 − [(x2)/2!] + [(x4)/4!] − [(x6)/6!])
  • = 0 − [2x/2!] + [(4x3)/4!] − [(6x5)/6!]
−x + [(x3)/3!] − [(x5)/5!]
NOTE: y in this problem is a truncated version of the series representation of cos(x).
Find the derivative of y = 1 + x + [(x2)/2!] + [(x3)/3!] + [(x4)/4!]
  • dy = [d/dx] (1 + x + [(x2)/2!] + [(x3)/3!] + [(x4)/4!])
1 + x + [(x2)/2!] + [(x3)/3!]
NOTE: y in this problem is a truncated version of the series representation of ex.

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Power Rule

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  • Intro 0:00
  • Power Rule 0:07
    • Power Rule Definition
  • Example 1 1:11
  • Example 2 2:25
  • Example 3 3:05
  • Example 4 4:18
  • Example 5 5:13

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