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lecture28

# lecture28 - Lecture 28 1 Lecture 28(Sec 5.5 Dierentiation...

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Lecture 28 1 Lecture 28: (Sec. 5.5) Differentiation of Logarithmic Functions How do we find the derivative of f ( x ) = ln x ? We have: d dx (ln x ) = NOTE:

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Lecture 28 2 ex. Find each x -value at which the graph of f ( x ) = x ln x has a horizontal tangent line. Then find the relative extrema of f .
Lecture 28 3 The Chain Rule for Logarithmic Functions Let f be a differentiable function of x . Then for f ( x ) > 0, d dx [ln( f ( x ))] = ex. d dx [ln(2 x x 2 )] =

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Lecture 28 4 Recall some basic Properties of the Natural Loga- rithm: 1) domain: 2) ln 1 = 3) ln e = 4) The Inverse Properties 5) ln ( xy ) = 6) ln ( x y ) = 7) ln ( x y ) =
Lecture 28 5 ex. Find f ( x ) for each of the following: 1) f ( x ) = ln x 2) f ( x ) = ln( x 2 + 1) 3 3) f ( x ) = [ln( x 2 + 1)] 3

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Lecture 28 6 ex. Find the equation of the tangent line to f ( x ) = ln(ln x ) at x = e .
Lecture 28 7 Simplifying before Differentiating ex. Find f ( x ) for f ( x ) = ln parenleftBigg

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lecture28 - Lecture 28 1 Lecture 28(Sec 5.5 Dierentiation...

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