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Simplifying Derivatives with Logarithmic Differentiation

Learn how to simplify derivatives of complicated functions involving products, quotients, or powers using logarithmic differentiation with examples and explanations. Explore the method in Sec.3.8 on Derivatives of Inverse Functions and Logarithms.

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Simplifying Derivatives with Logarithmic Differentiation

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  1. Sec 3.8: Derivatives of Inverse Functions and Logarithms Example: Remark:

  2. Sec 3.8: Derivatives of Inverse Functions and Logarithms Example: Example: Property: Differentiate both sides w.r.t x Chain rule

  3. Sec 3.8: Derivatives of Inverse Functions and Logarithms

  4. Sec 3.8: Derivatives of Inverse Functions and Logarithms Example:

  5. Sec 3.8: Derivatives of Inverse Functions and Logarithms Example:

  6. Sec 3.8: Derivatives of Inverse Functions and Logarithms Example: Example:

  7. Sec 3.8: Derivatives of Inverse Functions and Logarithms

  8. Sec 3.8: Derivatives of Inverse Functions and Logarithms Prop: Example:

  9. Sec 3.8: Derivatives of Inverse Functions and Logarithms Example:

  10. Sec 3.8: Derivatives of Inverse Functions and Logarithms Example:

  11. Sec 3.8: Derivatives of Inverse Functions and Logarithms The calculation of derivatives of complicated functions involving products, quotients, or powers can often be simplified by taking logarithms. The method used in the following example is called logarithmic differentiation.

  12. Sec 3.8: Derivatives of Inverse Functions and Logarithms

  13. Sec 3.8: Derivatives of Inverse Functions and Logarithms Example: If variables appear in the base and in the exponent : logarithmic differentiation can be used in this case

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