A x 2017 Special Derivatives e x, a x, ln (x), log a x AP Calculus.

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Presentation transcript:

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 a x, ln (x), log a x REM: IFF Two Properties from the Definition: ALSO: IFF Two Properties from the Definition:

Proof: ln(x)

ln(x) EX: EX: NOTE:

ln(x) EX: Find the second derivative.

Proof: a x

axax Ex:

Proof: log a (x)

log a (x)

Live Love Learn!

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

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 for dy/dx. Then resub for y.

Derivative : “Function raised to a Function Power”

Logarithmic Differentiation

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