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2017 Special Derivatives e x , a x , ln (x) , log a x

2017 Special Derivatives e x , a x , ln (x) , log a x. AP Calculus. Derivative of - Analytically. REM: . Chain Rule:. Ex:. a x , ln (x) , log a x. REM: IFF. Two Properties from the Definition:. ALSO: IFF.

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2017 Special Derivatives e x , a x , ln (x) , log a x

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  1. 2017 Special Derivativesex , ax , ln (x) , log ax AP Calculus

  2. Derivative of - Analytically REM: Chain Rule:

  3. Ex:

  4. ax , ln (x) , log ax REM: IFF Two Properties from the Definition: ALSO: IFF Two Properties from the Definition:

  5. Proof: ln(x)

  6. ln(x) EX: EX: NOTE:

  7. ln(x) EX: Find the second derivative.

  8. Proof: ax

  9. ax Ex:

  10. Proof: loga(x)

  11. loga(x)

  12. Live Love Learn!

  13. Logarithmic Differentiation REM: Properties of Logarithms Rewrite using properties of Logs.

  14. Logarithmic Differentiation Set the function equal to y. Take the natural log of both sides. Take the derivative of BOTH sides - f(y) and f(x) (implicitly) Solve fordy/dx. Thenresubfor y.

  15. Derivative : “Function raised to a Function Power”

  16. Logarithmic Differentiation

  17. Last Update • 10/20/10 • Assignment: p. 178 # 1 – 31 odd 43, 45

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