Home / Practice / Class 12 / Mathematics / Differentiation
Differentiation
6 Class 12 Mathematics questions with answers and explanations.
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All questions with answers
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The derivative of x^4 is:
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Correct answer: 4x^3
Power rule: n x^(n-1).
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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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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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The derivative of ln x is:
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Correct answer: 1/x
d/dx(ln x) = 1/x.
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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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The function f(x) = x2 - 4x has a minimum at x equal to:
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Correct answer: 2
f'(x) = 2x - 4 = 0 gives x = 2, and f'' = 2 is positive.
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