Calculus Mathematics Quiz: Differentiation Problems

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Janaisa Harris, BA (Mathematics) |
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Janaisa Harris, an experienced educator, has devoted 4 years to teaching high school math and 6 years to tutoring. She holds a bachelor's degree in Mathematics (Secondary Education, and Teaching) from the University of North Carolina at Greensboro and is currently employed at Wilson County School (NC) as a mathematics teacher.
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  • 1/10 Questions

    Differentiate y=2x4-4x+5

    • 8x4-4x
    • 8x3-4
    • 24x3+4
    • 8x4+4x
    • None of the above
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About This Quiz

Are you an expert in Calculus Mathematics? Would you like to try this calculus mathematics quiz: differentiation problems? We have an amazing calculus mathematics quiz for you, in which you can solve the Differentiation problems. You can answer the questions correctly to get your best score. These questions will also hone your math skills even further. So, have fun, check your knowledge and try to get the perfect score on the quiz.

Calculus Mathematics Quiz: Differentiation Problems - Quiz

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  • 2. 

    Differentiate y= -6x4+3x2-12x

    • 24x3-6x

    • -24x5+3x2-12x

    • -24x3+6x-12

    • 64x3-6x

    Correct Answer
    A. -24x3+6x-12
    Explanation
    The given expression y = -6x^4 + 3x^2 - 12x can be differentiated using the power rule of differentiation. The power rule states that for a term of the form ax^n, the derivative is given by nax^(n-1). Applying this rule to each term in the expression, we get the derivative as -24x^3 + 6x - 12.

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  • 3. 

    Differentiate of x6 is 6x, true or false?

    • True

    • False

    Correct Answer
    A. False
    Explanation
    The statement is false because the given differentiation is incorrect. The correct differentiation of x^6 is 6x^5.

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  • 4. 

    Differentiate of y= 3e-3x is -9e-3x true or false?

    • True

    • False

    Correct Answer
    A. True
    Explanation
    The given statement is true. The correct differentiation of y= 3e-3x is -9e-3x. This can be obtained by applying the power rule of differentiation, which states that the derivative of e^kx is k * e^kx. In this case, k is -3x, so the derivative becomes -3 * e^-3x. Simplifying further, we get -9e^-3x, which matches the given answer. Therefore, the statement is true.

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  • 5. 

    Differentiate y= tan (3x2-1)

    • Sec2 (3x2-1)

    • 6x sec2 (3x2-1)

    • 3x sec2 (3x2-10

    • Sec2 (3x-1)

    Correct Answer
    A. 6x sec2 (3x2-1)
    Explanation
    The correct answer is 6x sec^2(3x^2-1). To differentiate y = tan(3x^2-1), we can use the chain rule. The derivative of tan(u) is sec^2(u), and the derivative of (3x^2-1) with respect to x is 6x. Therefore, the derivative of y = tan(3x^2-1) is 6x sec^2(3x^2-1).

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  • 6. 

    Differentiate y=7x2 - 3e3x+1

    • 14 - 9e3x+1

    • 14x2-3e4x+1

    • 14x - 3e

    • 14x - 9e3x+1

    • None of the above

    Correct Answer
    A. 14x - 9e3x+1
    Explanation
    The given answer, 14x - 9e3x+1, is the correct differentiation of the function y=7x2 - 3e3x+1. The derivative of 7x2 is 14x, and the derivative of -3e3x+1 is -9e3x+1. Therefore, the correct answer is 14x - 9e3x+1.

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  • 7. 

    Which of the following represents the derivative of f(x) = x^3 * e^x ?

    • 3x^2 * e^x

    • X^3 * e^x + 3x^2 * e^x

    • X^3 * e^x - 3x^2 * e^x

    • E^x

    Correct Answer
    A. X^3 * e^x + 3x^2 * e^x
  • 8. 

    Differentiate y = x(3x2 - 5)

    • 9x2 -5x

    • 9x - 5

    • 6x 

    • 9x2 - 5

    • None of the above

    Correct Answer
    A. 9x2 - 5
    Explanation
    The correct answer is 9x^2 - 5. This is the correct answer because when we differentiate the given function, we use the power rule of differentiation. The power rule states that when differentiating a function of the form x^n, the derivative is nx^(n-1). Applying this rule to the given function, we differentiate the term 3x^2 to get 6x, and the constant term -5 differentiates to 0. Therefore, the derivative of y = x(3x^2 - 5) is 3x^2 + 6x - 5. Simplifying this expression gives us the correct answer of 9x^2 - 5.

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Janaisa Harris |BA (Mathematics) |
High School Math Teacher
Janaisa Harris, an experienced educator, has devoted 4 years to teaching high school math and 6 years to tutoring. She holds a bachelor's degree in Mathematics (Secondary Education, and Teaching) from the University of North Carolina at Greensboro and is currently employed at Wilson County School (NC) as a mathematics teacher.

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  • Dec 27, 2024
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  • Dec 29, 2020
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