Skip to content

Lars Eighner's Homepage


LarsWiki

calumus meretrix et gladio innocentis

Calculus Rule Exercises

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.

Basic Differentiation Exercises

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.)

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

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

worked

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

worked

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

worked

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:

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

Recommended:

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

Category: Math

About Math


Read or Post Comments

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

August 06, 2017

  • HomePage
  • WikiSandbox

Lars

Contact by Snail!

Lars Eighner
APT 1191
8800 N IH 35
AUSTIN TX 78753
USA

Help

HOME

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

Page List

Categories

Physics Pages

Math Pages

Math Exercises

Math Tools

Sections