Calculus Rules Practice
Authored by Emmanuel Yawiapui
Mathematics
12th Grade
Used 1+ times
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15 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Differentiate the function y = x^2 * e^x using the product rule.
y' = x^2 * e^x + e^x
y' = x^2 + 2x * e^x
y' = x^2 * e^x + x * e^x
y' = x^2 * e^x + 2x * e^x
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Find the derivative of y = (3x + 2) / (x - 1) using the quotient rule.
-3 / (x - 1)^2
-5 / (x - 1)^2
-2 / (x - 1)^2
5 / (x - 1)^2
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Calculate the derivative of y = sin(2x) using the chain rule.
2cos(x)
cos(2x)
2cos(2x)
4cos(2x)
sin(2x)
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Use the product rule to differentiate y = x^3 * cos(x).
y' = 3x^2 * sin(x) + x^3 * cos(x)
y' = 3x^2 * cos(x) + x^3 * sin(x)
y' = 3x^2 * sin(x) - x^3 * cos(x)
y' = 3x^2 * cos(x) - x^3 * sin(x)
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Apply the quotient rule to find the derivative of y = (2x^2 + 1) / (x^2 - 1).
(6x(x^2 - 1) + 2x(2x^2 + 1)) / (x^2 - 1)^2
(6x(x^2 - 1) - 2x(2x^2 - 1)) / (x^2 - 1)^2
(6x(x^2 + 1) - 2x(2x^2 - 1)) / (x^2 - 1)^2
(6x(x^2 - 1) - 2x(2x^2 + 1)) / (x^2 - 1)^2
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Find the derivative of y = e^(3x^2) using the chain rule.
6x * e^(3x^2)
3x * e^(3x^2)
9x * e^(3x^2)
6x^2 * e^(3x^2)
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Differentiate the function y = x^4 * ln(x) using the product rule.
4x^3 * ln(x) + 3x^2
4x^3 * ln(x) - x^3
4x^3 * ln(x) - 3x^2
4x^3 * ln(x) + x^3
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