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Exponentials and Logarithms Derivatives

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Agenda

  • Exponentials
  • Logarithms
  • Practice

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Exponentials

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Finding the Derivative

  • When finding the derivative of a function we can use the definition

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  • To get

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  • This looks a little messy - can we do better?

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Finding the Derivative

  • Starting with we see that the slope of the function at x=0 only depends on the base
  • Select the base so that its derivative is 1 at x=0
  • This base is called e
    • This is approx 2.718281828459045
    • Irrational and transcendental

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Finding the Derivative

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Logarithms

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Derivatives of Logarithms

  • Since logarithms are inverses of exponentials, it makes sense to look at the logarithm of base e
  • This is called the natural logarithm and is written ln x (pronounced “lawn of x”)
  • Go to the Jamboard D11 Examples Exponentials and Logarithms Derivatives

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Derivatives of Logarithms

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Practice

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Practice

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CREDITS

Special thanks to all the people who made and released these awesome resources for free:

  • Presentation template by SlidesCarnival

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