Differential Equations For Dummies
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In calculus, you often need to take higher order derivatives — that is, the derivative of a derivative, or the derivative of a derivative of a derivative, and so on. Why? Well, for example, a second derivative tells you the acceleration of a moving body.

So how do you do this? Simple! To find a higher order derivative, you just treat the first derivative as a new function and take its derivative in the ordinary way. You can keep doing this indefinitely. (Well, if you want to.)

The following practice questions won't ask you to go on indefinitely, but they will ask you to find third and fourth derivatives.

Practice questions

  1. For y = x5 + 10x3, find the 1st, 2nd, 3rd, and 4th derivatives.

  2. For y = cos (x2), find the 1st, 2nd, and 3rd derivatives.

Answers and explanations

  1. For y = x5 + 10x3, the 1st, 2nd, 3rd, and 4th derivatives are as follows:

    The higher order derivatives for y = x5 + 10x3
  2. For y = cos (x2), the 1st, 2nd, and 3rd derivatives are as follows:

    The first, second and third derivatives for y equals cos of squared x.

About This Article

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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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