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

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:

Recommended:

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

Category: Math

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.

### December 23, 2018

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