Main /

Exercises from public domain textbooks. Solutions where provided do not necessary follow the same lines as the original.

Solutions are not given for exercises whose number is not linked

Some solutions are given for exercises which do not have a textbook solution.

All of the following can be differentiated by inspection from the Differentiation Rules and Common Formulas. A few should be worked from the definition of derivative to be certain it is understood. Some solutions, where supplied, are in Leibniz notation. Recognize equivalent expressions in both notations.

(Note: Greek letters here are simply variables. In common usage Greek letters represent angles, but they are just variables nonetheless.)

A55-2. {$$ y= x^2 + 2 $$}

A55-3. {$$ y= 5 - 4x $$}

A55-4. {$$ s= 2t^2 - 4 $$}

A55-5. {$$ y= \frac{1}{x} $$}

A55-6. {$$ y= \frac{x + 2}{x} $$}

A55-7. {$$ y= x^3 $$}

A55-8. {$$ y= 2x^2 - 3 $$}

A55-9. {$$ y= 1 - 2x^3 $$}

A55-10. {$$ \rho= a\theta^2 $$}

A55-11. {$$ y= \frac{2}{x^2} $$}

A55-12. {$$ y= \frac{3}{x - 1} $$}

A55-13. {$$ y = 7x^2 + x$$}

A55-14. {$$ s = at^2 - 2bt$$}

A55-15. {$$ r = 8t + 3t^2$$}

A55-16. {$$ y = \frac{3}{x^2}$$}

A55-17. {$$ s = -\frac{a}{2t + 3}$$}

A55-18. {$$ y = bx^3 - cx$$}

A55-19. {$$ \rho = 3\theta^3 - 2\theta^2$$}

A55-20. {$$ y = \frac{3}{4}x^2 - \frac{1}{2}x$$}

A55-21. {$$ y = \frac{x^2 - 5}{x}$$}

A55-22. {$$ \rho = \frac{\theta^2}{1 + \theta}$$}

A55-23. {$$ y = \frac{1}{2}x^2 + 2x$$}

A55-24. {$$ z = 4x - 3x^2$$}

A55-25. {$$ \rho = 3\theta + \theta^2$$}

A55-26. {$$ y = \frac{ax + b}{x^2}$$}

A55-27. {$$ z = \frac{x^3 + 2}{x}$$}

A55-28. {$$ y = x^2 - 3x + 6 $$}

A55-29. {$$ s = 2t^2 + 5t - 8 $$}

A55-30. {$$ \rho = 5\theta^3 - 2\theta + 6 $$}

A55-31. {$$ y = ax^2 + bx + c $$}

The following are very heavy on the powers formula. Reviewing the Laws of Exponents might be helpful.

B24-1. {$$y = x^{13}$$} worked

B24-2. {$$y = x^{-\frac{3}{2}}$$}

B24-3. {$$y = x^{2a}$$}

B24-4. {$$u = t^{2.4}$$}

B24-5. {$$z = \sqrt[3]{u}$$}

B24-6. {$$y = \sqrt[3]{x^{-5}}$$}

B24-7. {$$u = \sqrt[5]{\dfrac{1}{x^8}}$$}

B24-8. {$$y = 2x^a$$}

B24-9. {$$y = \sqrt[q]{x^3}$$}

B24-10. {$$y = \sqrt[n]{\dfrac{1}{x^m}}$$}

*Sources:*

*Elements of the Differential and Integral Calculus***Wikisource***Calculus Made Easy*by Silvanus P. Thompson**Project Gutenberg**:

*Recommended:*

- Paul's Online Notes: Calculus I'' while not a source of material here, sometimes helpful when stuck.

**Category:** Math

- Derivative of 1/x from Definition.
- Derivative of Logarithm
- Geometric Interpretation of Derivative
- Implicit Differentiation
- Math Calculus Math Blackboard
- Math Styles
- MathJax Forms B
- MathJax Forms K
- MathJax Fragments
- MathJaxBlackboard
- MathJaxGraveyard
- Remedial Trigonometry
- Table of Derivatives
- Table of Derivatives, Integrals, & Constants
- Table of Integrals
- The Calculus of Single Variables

- Algebra Refresher Exercises Worked
- Calculus Polynomial Graph Exercises
- Calculus Polynomial Graph Exercises Answers
- Calculus Polynomial Graph Exercises Worked
- Calculus Rule Exercises
- Calculus Rule Exercises Answers
- Calculus Rule Exercises Worked
- Composite Exercises Answers
- Composite Function Exercises Worked
- Composition Function Exercises
- Implicit Differentiation Exercises
- Implicit Differentiation Exercises Answers
- Implicit Differentiation Exercises Worked
- Integration by Substitution Exercises
- Integration by Substitution Exercises Answers
- Integration by Substitution Exercises Worked
- Integration Exercises
- Integration Exercises Answers
- Integration Exercises Worked
- Limit Exercises
- Limit Exercises Answers
- Limit Exercises Worked
- Log and Exponential Differentiation Exercises
- Log and Exponential Differentiation Exercises Answers
- Log and Exponential Differentiation Exercises Worked

No comments yet.

This is a student's notebook. I am not responsible if you copy it for homework, and it turns out to be wrong.

Figures are often enhanced by hand editing; the same results may not be achieved with source sites and source apps.

**Backlinks**

This page is MathJacksonExercises

Lars

Contact by Snail!

Lars Eighner

APT 1191

8800 N IH 35

AUSTIN TX 78753

USA

Help

**The best way to look for anything in LarsWiki is to use the search bar.**

Physics Pages

- Classical Mechanics Bibliography
- Classical Mechanics Study Sources
- Physics About Physics
- Physics Classical Mechanics
- Physics Index
- Physics Quantum Notions
- Physics Template
- Quantum Physics
- Quantum Physics Bibliography
- Quantum Physics Study Sources
- Quantum Physics Syllabus
- Quarks
- Table of Physical Formulas & Constants
- The Blackbody Problem
- Units and Dimentional Analysis
- Vector Math for Quantum Mechanics

Math Pages

- Derivative of 1/x from Definition.
- (cos θ - 1) / θ = 1
- Algebra Example of Factoring
- Algebra Refresher Exercises
- Binomial Coefficients
- Binomial Theorem
- Coordinates Example
- Derivative of a Function at a Point
- Derivative of Logarithm
- Differential Sum Rule Demonstrated
- Differentiation
- Geometric Interpretation of Derivative
- Geometry
- Geometry of Trig Functions
- Graphing in Two Dimensions
- Hyperbolic Functions
- Implicit Differentiation
- Lim θ → 0 sin(θ) / θ = 1
- Linear Algebra
- Math About Math
- Math Analytic Geometry
- Math Formulas
- Math Function & Expression Index
- Math Index
- Math Markup
- Math Work Template
- Matrix Introduction
- Overview of The Calculus
- Remedial Trigonometry
- Table of Derivatives
- Table of Derivatives, Integrals, & Constants
- Table of Integrals
- Techniques of Integration
- The Calculus of Single Variables
- The Derivative of Arc Cotangent
- The Derivative of Arc Coversed Cosine
- The Derivative of Arc Coversed Sine
- The Derivative of Arc Versed Cosine
- The Derivative of Arc Versed Sine
- The Derivative of Arccosine
- The Derivative of Cosecant
- The Derivative of Cosine
- The Derivative of Cotangent
- The Derivative of Coversed Cosine
- The Derivative of Coversed Sine
- The Derivative of Haversed Sine
- The Derivative of Secant
- The Derivative of Sine
- The Derivative of Versed Cosine
- The Derivative of Versed Sine
- The Fundamental Theorem of Calculus
- The Witch of Agnesi
- Trigonometric Substitution Suggestions
- Vectors

Math Exercises

- Algebra Refresher Exercises Worked
- Calculus Polynomial Graph Exercises
- Calculus Polynomial Graph Exercises Answers
- Calculus Polynomial Graph Exercises Worked
- Calculus Rule Exercises
- Calculus Rule Exercises Answers
- Calculus Rule Exercises Worked
- Composite Exercises Answers
- Composite Function Exercises Worked
- Composition Function Exercises
- Implicit Differentiation Exercises
- Implicit Differentiation Exercises Answers
- Implicit Differentiation Exercises Worked
- Integration by Substitution Exercises
- Integration by Substitution Exercises Answers
- Integration by Substitution Exercises Worked
- Integration Exercises
- Integration Exercises Answers
- Integration Exercises Worked
- Limit Exercises
- Limit Exercises Answers
- Limit Exercises Worked
- Log and Exponential Differentiation Exercises
- Log and Exponential Differentiation Exercises Answers
- Log and Exponential Differentiation Exercises Worked

Math Tools

Sections