Derivatives Of Exponential And Logarithmic Functions Quiz Questions

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Derivatives Of Exponential And Logarithmic Functions Quiz Questions - Quiz

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!


Questions and Answers
  • 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-4x
    Explanation
    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).

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  • 2. 

    Is differentiation of e5x-1 is 5e5x-1 true or false?

    • A.

      True

    • B.

      False

    Correct Answer
    A. True
    Explanation
    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.

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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+2
    Explanation
    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.

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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= -3e2-3x
    Explanation
    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.

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  • 5. 

    Is differentiation of e1+5x is -5e1+5x true or false?

    • A.

      True

    • B.

      False

    Correct Answer
    B. False
    Explanation
    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.

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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).

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  • 7. 

    Is Differentiation of ln(5x) is 1/x true or false?

    • A.

      True

    • B.

      False

    Correct Answer
    A. True
    Explanation
    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.

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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).

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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. False
    Explanation
    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).

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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).

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  • Current Version
  • Apr 14, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Apr 07, 2022
    Quiz Created by
    Alfredhook3
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