Trigonometry Workbook For Dummies
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Differentiating exponential and logarithmic functions involves special rules. No worries — once you memorize a couple of rules, differentiating these functions is a piece of cake.

  • Exponential functions: If you can’t memorize this rule, hang up your calculator.

    image0.png

    Look at the graph of y = ex in the following figure.

    image1.jpg

    Pick any point on this function, say (2, ~7.4). The height of the function at that point, ~7.4, is the same as the slope at that point.

    If the base of the logarithmic function is a number other than e, you have to tweak the derivative by multiplying it by the natural log of the base. Thus,

    image2.png
  • Logarithmic functions: And now — can you guess? — the derivatives of logarithmic functions. Here’s the derivative of the natural log — that’s the log with base e:

    image3.png

    If the log base is a number other than e, you tweak this derivative — like with exponential functions — except that you divide by the natural log of the base instead of multiplying. Thus,

    image4.png

About This Article

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About the book author:

Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of several For Dummies books, including Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook For Dummies.

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