Derivatives of Logarithmic Functions
This worksheet focuses on understanding and calculating derivatives of logarithmic functions for Grade 9 Calculus students.
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Topics
Derivatives of Logarithmic Functions
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Carefully read each question and provide your answers in the space provided. Show all your work for full credit.
1. What is the derivative of f(x) = ln(x)?
x
1/x
e^x
ln(x)
2. If f(x) = log_a(x), then f'(x) is equal to:
1/(x * ln(a))
x * ln(a)
1/x
a^x
3. The derivative of ln(u) with respect to x, where u is a function of x, is .
4. The natural logarithm function is denoted by .
5. Find the derivative of y = ln(2x+1).
6. Differentiate f(x) = x^2 * ln(x).
7. The derivative of y = ln(x^2) is 2/x.
True
False
8. The derivative of log_10(x) is 1/(x * ln(10)).
True
False
9. A function is given by g(x) = ln(sqrt(x)). Find g'(x).
10. If y = (ln x)^3, find dy/dx.
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