Derivatives of Logarithmic Functions
Practice worksheet on finding derivatives of logarithmic functions, including natural logarithms and those with various bases.
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Standards
Derivatives of Logarithmic Functions
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Read each question carefully and find the derivative of the given logarithmic function. Show all your work.
1. Find the derivative of $y = \ln(x^2 + 1)$.
2. Differentiate $f(x) = \log_3(4x - 5)$.
3. If $g(x) = x^2 \ln(x)$, find $g'(x)$.
4. The derivative of $\ln(u)$ with respect to $x$ is .
5. The derivative of $\log_a(x)$ is .
6. The derivative of $y = \ln(5x)$ is $\frac{1}{5x}$.
True
False
7. The derivative of $f(x) = \log_{10}(x)$ is $\frac{1}{x \ln(10)}$.
True
False
8. Which of the following is the derivative of $y = \ln(\sin(x))$?
$-\cot(x)$
$\cot(x)$
$\frac{1}{\sin(x)}$
$\frac{\cos(x)}{\ln(\sin(x))}$
9. The derivative of $h(x) = \log_5(x^3)$ is:
$\frac{3}{x \ln(5)}$
$\frac{3x^2}{x^3 \ln(5)}$
$\frac{1}{x^3 \ln(5)}$
$\frac{3 \ln(5)}{x}$
10. Find the derivative of $y = \ln(\sqrt{x^2 + 1})$.
11. Differentiate $f(x) = \log(e^x + e^{-x})$. (Assume natural logarithm if base is not specified)