10.4 Derivative of Log Functions
Chapter
Chapter 10
Section
10.4
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Solutions 28 Videos

Determine \frac{dy}{dx}.

y = \log_5x

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0.17mins
Q1a

Determine \frac{dy}{dx}.

y = \log_3x

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Q1b

Determine \frac{dy}{dx}.

y = 2\log_4x

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0.30mins
Q1c

Determine \frac{dy}{dx}.

y = -3\log_7x

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Q1d

Determine \frac{dy}{dx}.

y = -(\log x)

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0.13mins
Q1e

Determine \frac{dy}{dx}.

y = 3\log_6x

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Q1f

Determine the derivative.

y = \log_3(x + 2)

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0.11mins
Q2a

Determine the derivative.

y = \log_8(2x)

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Q2b

Determine the derivative.

\displaystyle y = - 3\log_3(2x + 3)

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0.27mins
Q2c

Determine the derivative.

y = \log_{10}(5-2x)

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Q2d

Determine the derivative.

y = \log_8(2x+ 6)

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0.39mins
Q2e

Determine the derivative.

y = \log_{7}(x^2 + x + 1)

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Q2f

If f(t) = \log_2(\frac{t + 1}{2t + 7}), evaluate f'(3).

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1.41mins
Q3a

If h(t) = \log_3(\log_2(t)), determine h'(8).

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1.11mins
Q3b

Differentiate.

\displaystyle f(x) = \log_{10}(\frac{1 + x }{1- x})

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1.11mins
Q4a

Differentiate.

\displaystyle y = \log_2\sqrt{x^2 + 3x}

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1.46mins
Q4b

Differentiate.

\displaystyle y = 2\log_3(5^x) -\log_3(4^x)

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0.50mins
Q4c

Differentiate.

\displaystyle g(x) = 3^x\log_3x

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0.48mins
Q4d

Differentiate.

\displaystyle y = 2x \log_4x

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0.46mins
Q4e

Differentiate.

\displaystyle y = \frac{\log_5(3x^2)}{\sqrt{x + 1}}

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2.34mins
Q4f

Determine the equation of the tangent to the curve y = x\log x at x = 10. Graph the function and the tangent.

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1.08mins
Q5

Explain why the derivative of y = \log_akx, k > 0, is \frac{dy}{dx} = \frac{1}{x\ln a} for any constant k.

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Q6

Determine the domain, critical numbers, and intervals of increase and decrease of f(x) = \ln(x^2 -4).

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Q10

Do the graphs of either of these functions have points of inflection? Justify your answers with supporting calculations.

a) y = x\ln x

b) y = 3-2\log x

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Q11

Determine whether the slope of the graph of y = 3^x at the point (0, 1) is greater than the slope of the graph of y = \log_3x at the point (1, 0).

Include graphs with your solution.

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Q12