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Differentiation of Logarithmic Functions in Calculus

Learn how to differentiate various logarithmic functions in Calculus, such as ln(x) and log(u), using methods like implicit differentiation. Practice problems included!

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Differentiation of Logarithmic Functions in Calculus

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  1. Calculus Section 5.4Differentiate logarithmic functions If f(x) = ln x then f’(x) = 1/x y = 6 (ln x)3 Find the derivative. f(x) = x2ln x

  2. If f(x) = ln u, then f’(x) = 1/u Find the derivative. y = ln (x2 + 1) y = ln [(x3 + 9)5]

  3. Find the relative extrema. f(x) = 2x – ln (2x)

  4. Use implicit differentiation. 3x + y + ln y = 0

  5. If f(x) = logau, then f’(x) = 1/u Find the derivative. y = log5(x2 + 1)

  6. Find the derivative y = xx

  7. Assignment Page 295 Problems 2 -28 even, 36 – 52 even, 58 -70 even, 74,76

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