Q. If f(x) = x^4 - 2x^3 + x, what is f'(1)? (2023)
Solution
First, find f'(x) = 4x^3 - 6x^2 + 1. Then, f'(1) = 4(1)^3 - 6(1)^2 + 1 = 4 - 6 + 1 = -1.
Correct Answer:
A
— 2
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Q. If h(x) = e^(2x), what is h'(x)? (2019)
-
A.
2e^(2x)
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B.
e^(2x)
-
C.
2xe^(2x)
-
D.
e^(x)
Solution
Using the chain rule, h'(x) = 2e^(2x).
Correct Answer:
A
— 2e^(2x)
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Q. What is the derivative of f(x) = 3x^4 - 5x^2 + 2? (2021)
-
A.
12x^3 - 10x
-
B.
12x^3 - 5
-
C.
6x^3 - 5x
-
D.
3x^3 - 5
Solution
Using the power rule, f'(x) = 12x^3 - 10x.
Correct Answer:
A
— 12x^3 - 10x
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Q. What is the derivative of f(x) = 3x^4 - 5x^3 + 2x - 7?
-
A.
12x^3 - 15x^2 + 2
-
B.
12x^3 - 15x^2 - 2
-
C.
3x^3 - 5x^2 + 2
-
D.
3x^3 - 5x^2 - 2
Solution
Using the power rule, f'(x) = 12x^3 - 15x^2 + 2.
Correct Answer:
A
— 12x^3 - 15x^2 + 2
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Q. What is the derivative of f(x) = 4/x? (2022)
-
A.
-4/x^2
-
B.
4/x^2
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C.
-4/x
-
D.
4/x
Solution
Using the power rule, f'(x) = -4/x^2.
Correct Answer:
A
— -4/x^2
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Q. What is the derivative of f(x) = 5x^2 - 4x + 3?
-
A.
10x - 4
-
B.
10x + 4
-
C.
5x - 4
-
D.
5x + 4
Solution
Using the power rule, f'(x) = 10x - 4.
Correct Answer:
A
— 10x - 4
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Q. What is the derivative of f(x) = 5x^5 - 3x + 7? (2020)
-
A.
25x^4 - 3
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B.
15x^4 - 3
-
C.
5x^4 - 3
-
D.
20x^4 - 3
Solution
Using the power rule, f'(x) = 25x^4 - 3.
Correct Answer:
A
— 25x^4 - 3
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Q. What is the derivative of f(x) = 7x^2 + 2x - 5? (2023)
-
A.
14x + 2
-
B.
14x - 2
-
C.
7x + 2
-
D.
2x - 5
Solution
Using the power rule, f'(x) = 14x + 2.
Correct Answer:
A
— 14x + 2
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Q. What is the derivative of f(x) = x^2 * sin(x)? (2023)
-
A.
2x * sin(x) + x^2 * cos(x)
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B.
2x * cos(x) + x^2 * sin(x)
-
C.
2x * sin(x) - x^2 * cos(x)
-
D.
x^2 * sin(x) + 2x * cos(x)
Solution
Using the product rule, f'(x) = 2x * sin(x) + x^2 * cos(x).
Correct Answer:
A
— 2x * sin(x) + x^2 * cos(x)
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Q. What is the derivative of f(x) = x^3 * e^x?
-
A.
3x^2 * e^x + x^3 * e^x
-
B.
x^3 * e^x
-
C.
3x^2 * e^x
-
D.
x^3 * e^(x+1)
Solution
Using the product rule, f'(x) = 3x^2 * e^x + x^3 * e^x.
Correct Answer:
A
— 3x^2 * e^x + x^3 * e^x
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Q. What is the derivative of f(x) = x^3 * ln(x)? (2023)
-
A.
3x^2 * ln(x) + x^2
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B.
3x^2 * ln(x) + x^3/x
-
C.
3x^2 * ln(x) + 3x^2
-
D.
3x^2 * ln(x) + 1
Solution
Using the product rule, f'(x) = 3x^2 * ln(x) + x^2.
Correct Answer:
A
— 3x^2 * ln(x) + x^2
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Q. What is the derivative of f(x) = x^3 - 4x + 7? (2021)
-
A.
3x^2 - 4
-
B.
3x^2 + 4
-
C.
x^2 - 4
-
D.
3x^2 - 7
Solution
Using the power rule, f'(x) = 3x^2 - 4.
Correct Answer:
A
— 3x^2 - 4
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Q. What is the derivative of f(x) = x^4 - 6x^2 + 9? (2022)
-
A.
4x^3 - 12x
-
B.
4x^3 + 12x
-
C.
2x^3 - 6x
-
D.
2x^3 + 6x
Solution
Using the power rule, f'(x) = 4x^3 - 12x.
Correct Answer:
A
— 4x^3 - 12x
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