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3.9: Derivatives of Exponential and Log Functions Objective: To find and apply the derivatives of exponential and logarithmic functions

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QUICK REVIEW….. Properties of logs and exponential functions

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Derivative of e x Important limit: Proof:

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If u is a differentiable function of x, then Examples: Find y’.

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Derivative of a x Assume a is positive, and different from 1 Use properties of logs to write a x in terms of e x :

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If u is a differentiable function of x, then: Examples: Find the derivative.

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At what point on the function y=4 t -5 does the tangent line have a slope of 15?

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Derivative of ln x : y=ln x e y =x Use implicit to differentiate:

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If u is a differentiable function of x and u>0, then: Examples: Find dy/dx.

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Derivative of log a x: Change of Base formula

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If u is a differentiable function of x and u>0, then: Examples: Find y’:, for a >0, a ≠ 1

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Find the derivative of the following functions.

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Find an equation of the tangent line to the graph of the function at the given point.

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Power Rule for Arbitrary Real Powers If u is a positive differentiable function of x and n is any real number, then u n is a differentiable function of x and

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Logarithmic Differentiation Find the derivative: y=(x-2) x+1 ← Notice x in base and exponent!! No rule for this!

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FIND DY/DX

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