Differentiation Quiz - CBSE Class 12 Mathematics

Free practice quiz: Differentiation (CBSE Class 12 Mathematics). 18 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

Sample questions

1. What is the derivative of f(x) = 5x^2?

   1. 10x
   2. 5x
   3. 2x
   4. x^2
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   Answer: A. 10x

   Using the power rule of differentiation, d/dx [x^n] = nx^(n-1). Here, n=2, so the derivative is 5 * 2 * x^(2-1) = 10x.

2. What is the derivative of f(x) = 4x^4 - 2x + 7?

   1. 16x^3 - 2
   2. 4x^3 - 2
   3. 4x^4 - 2
   4. 0
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   Answer: A. 16x^3 - 2

   To find the derivative, differentiate each term: d/dx [4x^4] = 16x^3, d/dx [-2x] = -2, and constant 7 differentiates to 0. Thus, f'(x) = 16x^3 - 2.

3. Determine the derivative of f(x) = ln(x).

   1. 1/x
   2. ln(x)
   3. e^x
   4. 0
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   Answer: A. 1/x

   The derivative of ln(x) is 1/x, which is a standard rule in calculus.

4. What is the derivative of f(x) = x^3 + 3x^2 - 4x + 5?

   1. 3x^2 + 6x - 4
   2. 3x^2 - 4
   3. 6x + 3
   4. 0
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   Answer: A. 3x^2 + 6x - 4

   Differentiate: d/dx [x^3] = 3x^2, d/dx [3x^2] = 6x, d/dx [-4x] = -4, and d/dx [5] = 0. So, f'(x) = 3x^2 + 6x - 4.

5. What is the derivative of f(x) = cos(3x)?

   1. -3sin(3x)
   2. 3sin(3x)
   3. -sin(3x)
   4. sin(3x)
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   Answer: A. -3sin(3x)

   Using the chain rule: d/dx[cos(u)] = -sin(u) * du/dx. Here u = 3x, thus du/dx = 3, leading to the result -3sin(3x).

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