Differential Equations For Dummies
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Calculus is the mathematics of change — so you need to know how to find the derivative of a parabola, which is a curve with a constantly changing slope.


The figure below shows the graph of the above parabola.


Notice how the parabola gets steeper and steeper as you go to the right. You can see from the graph that at the point (2, 1), the slope is 1; at (4, 4), the slope is 2; at (6, 9), the slope is 3, and so on.

x (horizontal position) 1 2 3 4 5 6 etc.
y (height) 0.25 1 2.25 4 6.25 9 etc.
1/2 x (slope) 0.5 1 1.5 2 2.5 3 etc.

Here’s the calculus. You write


And you say,


Or you can say,

  1. Take the power and put it in front of the coefficient.

  2. Multiply.


    (Note that this is only a temporary, interim result on the road to the solution below; by itself, it is meaningless.)

  3. Reduce the power by 1.

    In this example, the 2 becomes a 1. So the derivative is


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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