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§4.3 Derivatives of Logarithmic and Exponential Functions (Pages 261~272)

§4.3 Derivatives of Logarithmic and Exponential Functions (Pages 261~272). Lecture 11. Derivatives of Logarithms of Functions :. Original Rule Generalized Rule. Derivatives of Logarithms of Absolute Values :. Original Rule Generalized Rule.

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§4.3 Derivatives of Logarithmic and Exponential Functions (Pages 261~272)

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  1. §4.3 Derivatives of Logarithmic and Exponential Functions (Pages 261~272) Lecture 11 Derivatives of Logarithms of Functions: Original Rule Generalized Rule

  2. Derivatives of Logarithms of Absolute Values: Original Rule Generalized Rule Derivatives of Exponentials of Functions: Original Rule Generalized Rule

  3. Differentiation of Logarithmic Functions Derivative of the Natural Logarithm Generalized Rule for Natural Logarithm Functions If u is a differentiable function, then

  4. Examples Ex. Find the derivative of Ex. Find an equation of the tangent line to the graph of Slope: Equation:

  5. Differentiation of Logarithmic Functions Derivative of a Logarithmic Function: Generalized Rule for Logarithm Functions If u is a differentiable function, then

  6. Differentiation of Logarithmic Functions Ex.

  7. Derivative of Logarithms of Absolute Values Original Rule Generalized Rule These two graphs show that

  8. Derivative of Logarithms of Absolute Values Ex. Ex.

  9. Differentiation of Exponential Functions Derivative of ex: Generalized Rule for eu: If u is a differentiable function, then

  10. Derivatives of Exponential Functions Ex. Find the derivative of Ex. Find the derivative of

  11. Differentiation of Exponential Functions Derivative of bx: Generalized Rule for bu: If uis a differentiable function, then

  12. Derivatives of Exponential Functions Ex. Find the derivative of

  13. Example 5: Sales GrowthThe sales of the Cyberpunk II arcade video game can be modeled by the logistic curve Where q(t) is the total number of units sold t months after its introduction. How fast is the game selling 2 years after its introduction? Solution:

  14. Radioactive DecayPlutonium-239 has a half-life of 24,400 years. How fast is a lump of 10 grams decaying after 100 years? HW Problem 83: Hints:

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