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Differentiation

6 Class 12 Mathematics questions with answers and explanations.

Printable worksheet with answer key

All questions with answers
  1. The derivative of x^4 is:

    • 1 x^3
    • 2 3x^4
    • 3 4x^3
    • 4 4x^4
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    Correct answer: 4x^3

    Power rule: n x^(n-1).

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  2. The derivative of sin x is:

    • 1 -cos x
    • 2 -sin x
    • 3 cos x
    • 4 tan x
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    Correct answer: cos x

    d/dx(sin x) = cos x.

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  3. The derivative of e^x is:

    • 1 x e^(x-1)
    • 2 1
    • 3 ln x
    • 4 e^x
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    Correct answer: e^x

    e^x is its own derivative.

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  4. The derivative of ln x is:

    • 1 x
    • 2 1/x
    • 3 ln x / x
    • 4 e^x
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    Correct answer: 1/x

    d/dx(ln x) = 1/x.

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  5. If y = x2 sin x, then dy/dx is:

    • 1 x2 cos x
    • 2 2x sin x
    • 3 2x cos x
    • 4 2x sin x + x2 cos x
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    Correct answer: 2x sin x + x2 cos x

    Product rule: (2x)(sin x) + (x2)(cos x).

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  6. The function f(x) = x2 - 4x has a minimum at x equal to:

    • 1 -2
    • 2 0
    • 3 2
    • 4 4
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    Correct answer: 2

    f'(x) = 2x - 4 = 0 gives x = 2, and f'' = 2 is positive.

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