Calculus I

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Calculus I

• Differentiation Rules

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Section 3.6 The Logarithmic Function

• Theorem Let f(x) ln x. Then f(x)
• Special case Let f(x) ln(g(x)), then f(x)

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Section 3.6 The Logarithmic Function

• Differentiate the following functions.
• y ln(3x-5)
• y ln(cos x)
• y ex lnx ln(ex 3x 5 )
• 4)

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Section 3.6 The Logarithmic Function

• Example Find f(x) provided that
• f(x) ln(sec x tan x)

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Section 3.6 The Logarithmic Function

• Example Find an equation of the tangent line to
  the curve f(x) ln(x3 - 7) at (2, 0).

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Section 3.6 The Logarithmic Function

• Example of Logarithmic Differentiation
• Find the derivative of
• 1) y xcosx 2) y

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Section 3.6 The Logarithmic Function

• Reference
• Stewart, Single Variable Calculus
• Early Transcendentals