Derivatives Of Exponential And Logarithmic Functions Quiz Questions
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Take up this quiz to review your knowledge of derivatives of exponential and logarithmic functions by choosing suitable answers to the questions asked here. The logarithmic function is the inverse of the exponential function. If you think your calculus is really strong and can score well on the test, why don't you clear out your doubt now? Also, the quiz will check your differentiating skills. Shall we start the quiz then? Give your best!
- 1.
Differentiate y= 3e-4x
- A.
Dy/dx = -3e-3x
- B.
Dy/dx= -12e4x
- C.
Dy/dx= -12e-4x
- D.
Dy/dx = 34e4x
Correct Answer
C. Dy/dx= -12e-4xExplanation
The given function is y = 3e^(-4x). To differentiate this function with respect to x, we use the chain rule. The derivative of e^(-4x) is -4e^(-4x) and the derivative of 3 is 0. Therefore, the derivative of y with respect to x is dy/dx = 0 * e^(-4x) + 3 * (-4e^(-4x)) = -12e^(-4x).Rate this question:
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- 2.
Is differentiation of e5x-1 is 5e5x-1 true or false?
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
The differentiation of e^5x-1 is 5e^5x-1. This can be derived using the chain rule of differentiation. The derivative of e^u is e^u times the derivative of u, which in this case is 5. Therefore, the correct answer is true.Rate this question:
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- 3.
Differentiate y= 2e5x+2
- A.
Dy/dx= -10e5x
- B.
Dy/dx= 10e5x+2
- C.
Dy/dx= 2e5x
- D.
Dy/dx= e5x+2
Correct Answer
B. Dy/dx= 10e5x+2Explanation
The correct answer is dy/dx= 10e5x+2. This is the correct answer because when differentiating y= 2e5x+2 with respect to x, the derivative of e5x is 5e5x and the derivative of 2 is 0. Therefore, the derivative of y with respect to x is 5e5x. Additionally, the constant term 2 remains unchanged. So the final answer is dy/dx= 10e5x+2.Rate this question:
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- 4.
Differentiate y= e2-3x
- A.
Dy/dx= 3e
- B.
Dy/dx= 3e2-3x
- C.
Dy/dx= 2e2-3x
- D.
Dy/dx= -3e2-3x
Correct Answer
D. Dy/dx= -3e2-3xExplanation
The correct answer is dy/dx= -3e^2-3x. To differentiate y = e^2-3x, we need to apply the chain rule. The derivative of e^2-3x with respect to x is -3e^2-3x.Rate this question:
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- 5.
Is differentiation of e1+5x is -5e1+5x true or false?
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
The statement "Differentiation of e1+5x is -5e1+5x" is false. When differentiating e1+5x, the derivative of e1 is 0 since e1 is a constant. The derivative of 5x is simply 5. Therefore, the correct answer is false.Rate this question:
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- 6.
Differentiate y= ln(7x+2)
- A.
Dy/dx = 7 /(7x+2)
- B.
Dy/dx= 2/(7x+2)
- C.
Dy/dx= 7(7x+2)
- D.
Dy/dx= 7x+2
Correct Answer
A. Dy/dx = 7 /(7x+2)Explanation
The correct answer is dy/dx = 7 /(7x+2). This is the correct differentiation of the given function y= ln(7x+2). The derivative of ln(u) with respect to x is du/dx divided by u. In this case, u = 7x+2, so du/dx = 7. Therefore, the derivative of ln(7x+2) with respect to x is 7/(7x+2).Rate this question:
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- 7.
Is Differentiation of ln(5x) is 1/x true or false?
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
The differentiation of ln(5x) can be found using the chain rule. The derivative of ln(u) is 1/u multiplied by the derivative of u with respect to x. In this case, u = 5x. So, the derivative of ln(5x) is 1/(5x) multiplied by the derivative of 5x, which is 5. Simplifying further, we get 1/x. Therefore, the statement "Differentiation of ln(5x) is 1/x" is true.Rate this question:
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- 8.
Differentiate y =ln(x-8)
- A.
Dy/dx= 1
- B.
Dy/dx = 1/(x-8)
- C.
Dy/dx= 8/(x-8)
- D.
Dy/dx= -1/(x-8)
Correct Answer
B. Dy/dx = 1/(x-8)Explanation
The derivative of ln(x-8) with respect to x is 1/(x-8). This can be found using the chain rule, where the derivative of ln(u) with respect to u is 1/u, and the derivative of (x-8) with respect to x is 1. Therefore, the derivative of ln(x-8) is 1/(x-8).Rate this question:
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- 9.
Is differentiation of ln(4x2-1) is 4x/(4x2-1) true or false?
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
The differentiation of ln(4x^2-1) is not equal to 4x/(4x^2-1). The correct answer is false. To differentiate ln(4x^2-1), we need to apply the chain rule. The derivative of ln(u) is 1/u multiplied by the derivative of u with respect to x. Therefore, the correct differentiation of ln(4x^2-1) is (8x)/(4x^2-1).Rate this question:
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- 10.
Differentiate y= ln(2+3x2)
- A.
Dy/dx= 6x
- B.
Dy/dx= 3x/(2+3x)
- C.
Dy/dx= 2/(2+3x2)
- D.
Dy/dx= 6x/(2+3x2)
Correct Answer
D. Dy/dx= 6x/(2+3x2)Explanation
The given problem asks us to differentiate the function y = ln(2 + 3x^2). To do this, we can use the chain rule. Taking the derivative of the function with respect to x, we get dy/dx = (2(3x))/(2 + 3x^2). Simplifying further, we have dy/dx = 6x/(2 + 3x^2). So, the correct answer is dy/dx = 6x/(2 + 3x^2).Rate this question:
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Apr 14, 2023Quiz Edited by
ProProfs Editorial Team -
Apr 07, 2022Quiz Created by
Alfredhook3
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