Tag Archives: differential calculus solutions

$Cover photo of Chapter 8: Partial Differentiation of the book Differential and Integral Calculus by Feliciano and Uy$

Chapter 8: Partial Differentiation

8.1 Partial Derivative

8.2 Geometric Interpretation of Partial Derivative

Exercise 8.1

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

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8.3 Partial Derivatives of Higher Order

Exercise 8.2

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

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8.4 Total Differentiation

Exercise 8.3

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

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8.5 Total Derivative

Exercise 8.4

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

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8.6 Partial Differentiation of Implicit Functions

Exercise 8.5

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

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8.7 Tangent Plane and Normal Line

Exercise 8.6

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

8.8 Maxima and Minima

Exercise 8.7

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

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$Cover photo of Chapter 7: Derivatives from Parametric Equations, Radius and Center of Curvature of the book Differential and Integral Calculus by Feliciano and Uy$

Chapter 7: Derivatives from Parametric Equations, Radius and Center of Curvature

7.1 Derivatives in Parametric Form

Exercise 7.1

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

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7.2 Differential of Arc Length

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7.3 Radius of Curvature

Exercise 7.2

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

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7.4 Center of Curvature

Exercise 7.2

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

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$Cover photo of Chapter 6 The Differential of the book Differential and Integral Calculus by Feliciano and Uy$

Chapter 6: The Differential

6.1 Differential: Definition and Interpretation

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6.2 Differential Formulas

Exercise 6.1

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

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6.3 Applications of the Differential

Exercise 6.2

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

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$Cover photo of Chapter 5 The Indeterminate Forms of the book Differential and Integral Calculus by Feliciano and Uy$

Chapter 5: The Indeterminate Forms

5.1 Rolle’s Theorem

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5.2 Mean Value Theorem

Exercise 5.1

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

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5.3 L’Hospital’s Rule

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5.4 The Indeterminate Forms $\displaystyle \frac{0}{0}$ and $\displaystyle \frac{\infty }{\infty }$

Exercise 5.2

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

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5.5 The Indeterminate Forms $\displaystyle 0\left( \pm \infty \right)$ and $\displaystyle \infty -\infty$

Exercise 5.3

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

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5.6 The Indeterminate Forms $\displaystyle 0^0$ , $\displaystyle 1^\infty$ , and $\displaystyle \infty ^0$

Exercise 5.4

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

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$Cover photo of Chapter 4 Differentiation of Transcendental Functions of the book Differential and Integral Calculus by Feliciano and Uy$

Chapter 4: Differentiation of Transcendental Functions

4.1 The Function $\displaystyle \frac{\sin u}{u}$

Exercise 4.1

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

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4.2 Differentiation of Trigonometric Functions

Exercise 4.2

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

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4.3 Differentiation of Inverse Trigonometric Functions

Exercise 4.3

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

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4.4 The functions $\displaystyle \left( 1+u \right)^{\frac{1}{u}}$

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4.5 The Logarithmic and Exponential Functions

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4.6 Differentiation of Logarithmic Functions

Exercise 4.4

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

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4.7 Logarithmic Differentiations

Exercise 4.5

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

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4.8 Differentiation of Exponential Functions

Exercise 4.6

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

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4.9 The Hyperbolic Functions

Exercise 4.7

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

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4.10 Differentiation of Hyperbolic Functions

Exercise 4.8

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

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4.11 Differentiation of Inverse Hyperbolic Functions

Exercise 4.9

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

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$Cover photo of Chapter 3 Some Applications of the Derivatives of the textbook Differential and Integral Calculus by Feliciano and Uy$

Chapter 3: Some Applications of the Derivative

3.1 Equations of Tangents and Normals

Exercise 3.1

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

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3.2 Angle Between Two Curves

Exercise 3.2

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

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3.3 Increasing and Decreasing Functions

Exercise 3.3

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

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3.4 Maximum and Minimum Values of a Function

Exercise 3.4

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

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3.5 Significance of the Second Derivative

Exercise 3.5

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

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3.6 Applications of the Maxima and Minima

Exercise 3.6

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

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3.7 Related Rates

Exercise 3.7

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

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3.8 Rectilinear Motion

Exercise 3.7

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

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$Cover photo for Chapter 2 Differentiation of Algebraic Functions of the textbook Differential and Integral Calculus by Feliciano and Uy$

Chapter 2: Differentiation of Algebraic Functions

2.1 The Symbol Δ

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2.2 The Derivative of a Function

Exercise 2.1

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

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2.3 Geometric Significance of dy/dx

2.4 Rules for Differentiation

Exercise 2.2

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

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2.5 The Chain Rule

2.6 Differentiation of Inverse Functions

Exercise 2.3

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

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2.7 Higher Derivatives

Exercise 2.4

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

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2.8 Implicit Differentiation

Exercise 2.5

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

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Textbook Solutions for Calculus I

Differential and Integral Calculus by Feliciano and Uy

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Mathematics

Advanced Engineering Mathematics

Probability and Statistics

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$Cover photo for Chapter 1: Limits of the textbook Differential and Integral Calculus by Feliciano and Uy$

Chapter 1: Limits

Exercise 1.1: Functional Notation

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Exercise 1.2: Theorems on Limits

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Exercise 1.3: Indeterminate Forms

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Exercise 1.4: Limit at Infinity

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Exercise 1.5: Continuity

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

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Exercise 1.6: Asymptotes

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

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8.1 Partial Derivative

8.2 Geometric Interpretation of Partial Derivative

Exercise 8.1

8.3 Partial Derivatives of Higher Order

Exercise 8.2

8.4 Total Differentiation

Exercise 8.3

8.5 Total Derivative

Exercise 8.4

8.6 Partial Differentiation of Implicit Functions

Exercise 8.5

8.7 Tangent Plane and Normal Line

Exercise 8.6

8.8 Maxima and Minima

Exercise 8.7

7.1 Derivatives in Parametric Form

Exercise 7.1

7.2 Differential of Arc Length

7.3 Radius of Curvature

Exercise 7.2

7.4 Center of Curvature

Exercise 7.2

6.1 Differential: Definition and Interpretation

6.2 Differential Formulas

Exercise 6.1

6.3 Applications of the Differential

Exercise 6.2

5.1 Rolle’s Theorem

5.2 Mean Value Theorem

Exercise 5.1

5.3 L’Hospital’s Rule

5.4 The Indeterminate Forms \displaystyle \frac{0}{0} and \displaystyle \frac{\infty }{\infty }

Exercise 5.2

5.5 The Indeterminate Forms \displaystyle 0\left( \pm \infty \right) and \displaystyle \infty -\infty

Exercise 5.3

5.6 The Indeterminate Forms \displaystyle 0^0 , \displaystyle 1^\infty , and \displaystyle \infty ^0

Exercise 5.4

4.1 The Function \displaystyle \frac{\sin u}{u}

Exercise 4.1

4.2 Differentiation of Trigonometric Functions

Exercise 4.2

4.3 Differentiation of Inverse Trigonometric Functions

Exercise 4.3

4.4 The functions \displaystyle \left( 1+u \right)^{\frac{1}{u}}

4.5 The Logarithmic and Exponential Functions

4.6 Differentiation of Logarithmic Functions

Exercise 4.4

4.7 Logarithmic Differentiations

Exercise 4.5

4.8 Differentiation of Exponential Functions

Exercise 4.6

4.9 The Hyperbolic Functions

Exercise 4.7

4.10 Differentiation of Hyperbolic Functions

Exercise 4.8

4.11 Differentiation of Inverse Hyperbolic Functions

Exercise 4.9

3.1 Equations of Tangents and Normals

Exercise 3.1

3.2 Angle Between Two Curves

Exercise 3.2

3.3 Increasing and Decreasing Functions

Exercise 3.3

3.4 Maximum and Minimum Values of a Function

Exercise 3.4

3.5 Significance of the Second Derivative

Exercise 3.5

3.6 Applications of the Maxima and Minima

Exercise 3.6

3.7 Related Rates

Exercise 3.7

3.8 Rectilinear Motion

Exercise 3.7

2.1 The Symbol Δ

2.2 The Derivative of a Function

Exercise 2.1

2.3 Geometric Significance of dy/dx

2.4 Rules for Differentiation

Exercise 2.2

2.5 The Chain Rule

5.4 The Indeterminate Forms $\displaystyle \frac{0}{0}$ and $\displaystyle \frac{\infty }{\infty }$

5.5 The Indeterminate Forms $\displaystyle 0\left( \pm \infty \right)$ and $\displaystyle \infty -\infty$

5.6 The Indeterminate Forms $\displaystyle 0^0$ , $\displaystyle 1^\infty$ , and $\displaystyle \infty ^0$

4.1 The Function $\displaystyle \frac{\sin u}{u}$

4.4 The functions $\displaystyle \left( 1+u \right)^{\frac{1}{u}}$