
Mastering Derivatives and Logarithms
Authored by Puteri Mustapha
Mathematics
Professional Development

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16 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of ln(x) with respect to x?
1
1/x
ln(x)
x
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Apply the chain rule to find the derivative of ln(g(x)) where g(x) = x^2 + 3x.
(2x + 3) / (x^2 + 3x)
(2x + 3) / (x^2)
(2x + 3) / (2x + 3)
(x^2 + 3) / (2x + 3)
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Differentiate ln(x^2 + 1) using the chain rule.
2/(x^2 + 1)
x/(x^2 + 1)
2x/(x^2 + 1)
2x^2/(x^2 + 1)^2
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of ln(2x + 1)?
ln(2x + 1)
2/(2x + 1)
1/(2x + 1)
2x/(2x + 1)
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
If y = ln(x^2 + 4x + 4), what is dy/dx?
(2x + 4) / (x^2 + 4x + 4)
(x + 2) / (x^2 + 4)
(2x + 2) / (x^2 + 4x)
(4x + 4) / (x^2 + 4x + 4)
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Differentiate ln(3x^3 + 2) using implicit differentiation.
rac{3x^2}{3x^3 + 2}
rac{27x^3}{3x^3 + 2}
rac{9x^2}{6x^2}
\frac{9x^2}{3x^3 + 2}
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Find the derivative of ln(x + x^2 + 1) using the chain rule.
(2x) / (x + x^2 + 1)
(1 + 2x) / (x + x^2 + 1)
(1 + x^2) / (x + x^2 + 1)
(1 + x) / (x + x^2 + 1)
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