NUST NET Maths chapter 8: Maths · Differentiation MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

26 exam-style questions on Maths · Differentiation, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

26 questions · 2 topics · 10 per test

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What chapter 8 covers

Ten Maths · Differentiation questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. If y = xx (x > 0), then dy/dx equals

  1. A
    x · xx − 1
  2. B
    xx ln x
  3. C
    xx(1 + ln x)
  4. D
    xx(1 − ln x)
Show answer

Answer: C. Take logs: ln y = x ln x, so (1/y) dy/dx = ln x + 1 and dy/dx = xx(1 + ln x). The power rule and the ax rule each give only part of this.

2. The tangent to y = x2 − 3x is parallel to the line y = x + 7 at the point

  1. A
    (1, −2)
  2. B
    (2, 2)
  3. C
    (−1, 4)
  4. D
    (2, −2)
Show answer

Answer: D. Parallel lines have equal gradients: 2x − 3 = 1, so x = 2 and y = 4 − 6 = −2. At (1, −2) the gradient is −1, so that tangent is perpendicular to the line instead.

3. If y = ln(x2 + 1), then dy/dx equals

  1. A
    2x/(x2 + 1)
  2. B
    1/(x2 + 1)
  3. C
    2x ln(x2 + 1)
  4. D
    (x2 + 1)/(2x)
Show answer

Answer: A. Chain rule: d/dx ln u = u′/u = 2x/(x2 + 1). Forgetting to multiply by u′ = 2x gives 1/(x2 + 1).

4. If y = sin 2x, then d2y/dx2 + 4y equals

  1. A
    8 sin 2x
  2. B
    0
  3. C
    2 sin 2x
  4. D
    −8 sin 2x
Show answer

Answer: B. dy/dx = 2 cos 2x and d2y/dx2 = −4 sin 2x, so the sum is −4 sin 2x + 4 sin 2x = 0. A sign slip in the second derivative gives 8 sin 2x.

5. For the curve x2 + xy + y2 = 7, the value of dy/dx at the point (1, 2) is

  1. A
    −4/5
  2. B
    4/5
  3. C
    −5/4
  4. D
    −1/2
Show answer

Answer: A. Differentiate implicitly: 2x + y + x(dy/dx) + 2y(dy/dx) = 0, so dy/dx = −(2x + y)/(x + 2y) = −(2 + 2)/(1 + 4) = −4/5.

6. d/dx [sin−1(2x)] equals

  1. A
    2/√(1 − 4x2)
  2. B
    1/√(1 − 4x2)
  3. C
    −2/√(1 − 4x2)
  4. D
    2/√(1 − 2x2)
Show answer

Answer: A. d/dx sin−1 u = u′/√(1 − u2) with u = 2x and u′ = 2, giving 2/√(1 − 4x2). The minus sign belongs to the derivative of cos−1.

7. The local maximum value of f(x) = x3 − 3x is

  1. A
    2
  2. B
    −1
  3. C
    −2
  4. D
    1
Show answer

Answer: A. f′(x) = 3x2 − 3 = 0 at x = ±1. f″(−1) = −6 < 0, so x = −1 gives the maximum f(−1) = −1 + 3 = 2. −2 is the local minimum value, at x = 1.

8. Using differentials, the approximate value of √25.1 is

  1. A
    5.01
  2. B
    5.1
  3. C
    5.001
  4. D
    5.02
Show answer

Answer: A. With y = √x, dy = dx/(2√x) = 0.1/(2 × 5) = 0.01, so √25.1 ≈ 5 + 0.01 = 5.01. Forgetting the 2 in 2√x gives 5.02.

9. If x = t2 and y = t3, then dy/dx equals

  1. A
    2/(3t)
  2. B
    3t/2
  3. C
    3t2
  4. D
    2t/3
Show answer

Answer: B. dy/dx = (dy/dt) ÷ (dx/dt) = 3t2/(2t) = 3t/2. Dividing the other way round gives 2/(3t).

10. d/dx [x/(x + 1)] equals

  1. A
    1/(x + 1)2
  2. B
    −1/(x + 1)2
  3. C
    (2x + 1)/(x + 1)2
  4. D
    1
Show answer

Answer: A. Quotient rule: [(x + 1)(1) − x(1)]/(x + 1)2 = 1/(x + 1)2. Taking the numerator terms in the wrong order gives the minus sign; adding them gives (2x + 1)/(x + 1)2.

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Ways to practise this chapter

Maths · Differentiation: questions students ask

How many Maths · Differentiation MCQs are there?

26, each with the answer and a short explanation, across 2 topics: Rules of differentiation, Applications of derivatives. Every chapter test draws ten of them, so you can take it many times.

Is the NUST NET Maths chapter 8 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

Can I read the explanations in Urdu?

Yes. In practice mode and on your results you can switch the explanations to Urdu.

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