Differential Equations Workbook For Dummies
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According to the power rule, if you want to find the derivative of a variable raised to a power, you must bring the power in front — multiplying it by the coefficient, if there is one — and then reduce the power by one.

To see the power rule in action, take a look at the following practice questions.

Practice questions

  1. If f (x) = 5x4, then find the derivative,

    image0.png
  2. Find the derivative,

    image1.png

Answers and explanations

  1. The derivative of f (x) = 5x4 is

    image2.png

    To find the derivative, bring the 4 in front and multiply it by the 5, and at the same time reduce the power by 1, from 4 to 3:

    image3.png

    Notice that the coefficient 5 has no effect on how you do the derivative in the following sense: You could ignore the 5 temporarily, do the derivative of x4 (which is 4x3), and then put the 5 back where it was and multiply it by 4.

  2. The derivative is

    image4.png

    To find the derivative, first rewrite with an exponent

    image5.png

    Bring the power in front and reduce the power by one:

    image6.png

    To write your answer without a negative power, you write

    image7.png

    Or you can write your answer without a fraction power, to wit:

    image8.png

About This Article

This article is from the book:

About the book author:

Steven Holzner was an award-winning author of more than 130 books, of which more than 2 million copies have been sold. His books have been translated into 23 languages. He served on the Physics faculty at Cornell University for more than a decade, teaching both Physics 101 and Physics 102. Holzner received his doctorate in physics from Cornell and performed his undergraduate work at Massachusetts Institute of Technology, where he also served as a faculty member.

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