Derivatives of Logarithmic Functions
Explore and practice finding derivatives of logarithmic functions, including natural logarithms and those with various bases, suitable for Grade 11 Calculus students.
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Derivatives of Logarithmic Functions
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Read each question carefully and show all your work. Simplify your answers as much as possible.
1. Find the derivative of the function $f(x) = \ln(x^3 + 2x)$.
2. Differentiate $y = \log_5(4x^2 - 1)$.
3. The derivative of $f(x) = \ln(x)$ is $f'(x) = $ .
4. The derivative of $f(x) = \log_b(x)$ is $f'(x) = $ .
5. Which of the following is the derivative of $f(x) = x^2 \ln(x)$?
$2x \ln(x) - x$
$x \ln(x) + x$
$2x \ln(x) + x$
$2x \ln(x) + \frac{1}{x}$
6. Find the derivative of $g(x) = \ln(\frac{x^2+1}{x-3})$.
7. The derivative of $f(x) = \ln(e^x)$ is $f'(x) = 1$.
True
False