Section Summary: 7.4 - derivatives of logarithmic functions

  1. Definitions

  2. Theorems

  3. Properties/Tricks/Hints/Etc.

  4. Summary

    The derivative of the natural log function is easily obtained using a result from inverse functions: that

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    Since the natural log is the the inverse of the exponential function with base e, we have that

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    Simple! Furthermore, derivatives of compositions of functions with logarithms are easy to find. This is the mirror property of the simplicity of finding derivatives of compositions with exponential functions. It also gives rise to the idea of logarithmic differentiation, which uses the properties of logarithms to turn complicated quotient and product functions into simple functions whose derivatives can be found quickly and easily.

    Again, no need to worry about derivatives of other bases, since we can always replace an alien base with base e.

Problems:

Problems, pp. 443-444, #3, 4, 14, 20, 31, 36, 42, 62, 70, 82

On the board: 7, 11, 31, 32, 58, 67





LONG ANDREW E
Mon Apr 23 11:19:17 EDT 2001