Differentiation Practice Questions With Answers

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Mathematics Expert
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Ms. Janaisa Harris, an experienced educator, has devoted 4 years to teaching high school math and 6 years to tutoring. She holds a 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. She is now broadening her educational impact by engaging in curriculum mapping for her county. This endeavor enriches her understanding of educational strategies and their implementation. With a strong commitment to quality education, she actively participates in the review process of educational quizzes, ensuring accuracy and relevance to the curriculum.
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Differentiation Practice Questions With Answers - Quiz

Challenge your differentiation prowess with "Differentiation Practice Questions." This quiz offers an opportunity to gauge your competence in solving diverse differentiation problems. Whether you're a differentiation expert or seeking to bolster your understanding, this differentiation practice questions quiz caters to both needs.

Within the domain of mathematics, differentiation is the process of determining a function's derivative. The quiz will present you with intricate differentiation conundrums, testing the depth of your knowledge. Do you have the skills it takes? Engage with these differentiation practice questions to evaluate your calculus acumen, and don't forget to share this quiz to foster learning among Read morepeers.


Differentiation Practice Questions and Answers

  • 1. 

    Which method should we use for y=(x-2)3(x+1)?

    • A.

      Chain rule

    • B.

      Product Rule

    • C.

      Quotient Rule

    • D.

      Substitution method 

    Correct Answer
    B. Product Rule
    Explanation
    The given function y=(x-2)3(x+1) involves the multiplication of two functions, (x-2) and (x+1). Therefore, the appropriate method to differentiate this function is the Product Rule. The Product Rule states that when differentiating the product of two functions, u and v, the derivative is given by the first function times the derivative of the second function, plus the second function times the derivative of the first function. In this case, u = (x-2) and v = (x+1), so applying the Product Rule will yield the correct result.

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  • 2. 

    Which method should use for y = x5/(x-3)?

    • A.

      Chain Rule

    • B.

      Product Rule

    • C.

      Quotient Rule

    • D.

      Gauss Method

    Correct Answer
    C. Quotient Rule
    Explanation
    The given function is in the form of a quotient, where the numerator is x^5 and the denominator is (x-3). The Quotient Rule is used to differentiate such functions. According to the Quotient Rule, the derivative of a quotient is calculated by taking the derivative of the numerator (5x^4) multiplied by the denominator (x-3), minus the derivative of the denominator (1), multiplied by the numerator. Therefore, the Quotient Rule should be used to find the derivative of y = x^5/(x-3).

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  • 3. 

    The differentiation of 7x-3 is 21x-4.

    • A.

      True

    • B.

      False

    Correct Answer
    B. False
  • 4. 

    Differentiate y= -2x- 6x2 + 3.

    • A.

      12

    • B.

      2x4-12x2+3

    • C.

      10x4-12x

    • D.

      -10x4-12x

    Correct Answer
    D. -10x4-12x
    Explanation
    The given answer is obtained by differentiating the given function, y = -2x^5 - 6x^2 + 3, using the power rule of differentiation. According to this rule, when differentiating a term of the form ax^n, the derivative is obtained by multiplying the coefficient a by the exponent n and then subtracting 1 from the exponent. Applying this rule to each term in the function, we get -10x^4 - 12x. Therefore, the correct answer is -10x^4 - 12x.

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  • 5. 

    Y=x4(x-2)4 can be solved by Quotient Rule. True or false

    • A.

      True

    • B.

      False

    Correct Answer
    B. False
    Explanation
    The given expression y=x^4(x-2)^4 does not require the Quotient Rule to be solved. The Quotient Rule is used to differentiate functions that involve a quotient of two functions. In this case, there is no division involved, so the Quotient Rule is not applicable. Therefore, the correct answer is false.

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  • 6. 

    Y= (x+4)/(x-3)4 can be solved by Quotient Rule. True or false

    • A.

      True

    • B.

      False

    Correct Answer
    A. True
    Explanation
    The given equation y= (x+4)/(x-3) can be solved using the Quotient Rule, which is a method used to find the derivative of a function that is in the form of a quotient. The Quotient Rule states that if y= f(x)/g(x), then the derivative of y with respect to x is given by (g(x)f'(x) - f(x)g'(x))/(g(x))^2. Since the equation y= (x+4)/(x-3) is in the form of a quotient, it can be solved using the Quotient Rule. Therefore, the statement "y= (x+4)/(x-3) can be solved by Quotient Rule" is true.

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  • 7. 

    Differentiate y= 6x - sin (3x).

    • A.

      3 cos (3x)

    • B.

      6 - 3 cos (3x)

    • C.

      6 + cox (3x)

    • D.

      6 - cos (3x)

    Correct Answer
    B. 6 - 3 cos (3x)
    Explanation
    The correct answer is 6 - 3 cos (3x). To differentiate the given function, we first differentiate the term 6x, which gives us 6. Then, we differentiate the term -sin(3x) using the chain rule, which gives us -3 cos(3x). Therefore, the derivative of y = 6x - sin(3x) is 6 - 3 cos(3x).

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  • 8. 

    Differentiate y = 4x3 - e2x.

    • A.

      12x3- ex

    • B.

      12x2 - 2ex

    • C.

      12x- 2e2x

    • D.

      4x2 - 2e2x

    Correct Answer
    C. 12x- 2e2x
  • 9. 

    Differentiate y = x(x2-6).

    • A.

      6x

    • B.

      3x- 6

    • C.

      X2

    • D.

      X3 - 6x

    Correct Answer
    B. 3x- 6
    Explanation
    The correct answer is 3x^2 - 6. This is the correct differentiation of the given function y = x(x^2-6). To differentiate this function, we use the power rule and the product rule. The power rule states that the derivative of x^n is n*x^(n-1), and the product rule states that the derivative of the product of two functions is the first function multiplied by the derivative of the second function, plus the second function multiplied by the derivative of the first function. Applying these rules, we get the derivative of y = x(x^2-6) as 1*(x^2-6) + x*(2x) = x^2 - 6 + 2x^2 = 3x^2 - 6.

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Janaisa Harris |BA-Mathematics |
Mathematics Expert
Ms. Janaisa Harris, an experienced educator, has devoted 4 years to teaching high school math and 6 years to tutoring. She holds a 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. She is now broadening her educational impact by engaging in curriculum mapping for her county. This endeavor enriches her understanding of educational strategies and their implementation. With a strong commitment to quality education, she actively participates in the review process of educational quizzes, ensuring accuracy and relevance to the curriculum.

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  • Current Version
  • Apr 22, 2024
    Quiz Edited by
    ProProfs Editorial Team

    Expert Reviewed by
    Janaisa Harris
  • May 25, 2022
    Quiz Created by
    Catherine Halcomb
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