Q1. If y = 10x² then y₂ = ______
The first derivative is 20x, and the second derivative is 20, a constant.
class 12 Math Chapter 2: Differentiation MCQs With Explanations
Practice class 12 Math Chapter 2: Differentiation MCQs with explanations for Pakistani board exams. Includes solved objective questions, answer checking, chapter revision guidance and next chapter suggestions.
20 MCQs
Chapter 2: Differentiation Objective Preparation
Use this page for direct chapter practice, answer checking and explanation review. It is available through the clean URL shown in the browser, so students can bookmark and share this exact chapter.
20Total MCQs
20With explanations
1Topics represented
Topics found: Differentiation
Live Online MCQs Test
Create a custom, interactive chapter-wise MCQs quiz for quick revision and test practice.
Start Quiz
Differentiation MCQs With Explanations
Q2. y = xˣ has a minimum value at x =
By logarithmic differentiation, y = xˣ has a critical point at x = 1/e, which is a minimum as confirmed by the second derivative test.
Q3. Any point where f is neither increase nor decrease is called a point:
A stationary point occurs where the derivative is zero, meaning the function is neither increasing nor decreasing at that point.
Q4. f is said to be decreasing on (a, b) if f(x₁) < f(x₂) whenever:
A function is decreasing if a larger input produces a smaller output, so f(x₁) < f(x₂) when x₁ > x₂.
Q5. 1 + x + x²/2! + x³/3! + … is Maclaurin series of:
The Maclaurin series for eˣ is the sum of xⁿ/n! for n from 0 to infinity, which matches the given series term by term.
Q6. y''' represents the derivative:
Each prime symbol denotes one differentiation, so y''' is the third derivative of y.
Q7. d/dx (tanh⁻¹ x) =
The derivative of the inverse hyperbolic tangent function is 1/(1−x²) for |x| < 1, derived from its logarithmic definition and chain rule.
Q8. What is d/dx (sinh 2x)?
The derivative of sinh(u) is cosh(u) · u'. Here, u = 2x, so d/dx (sinh 2x) = cosh(2x) · 2 = 2 cosh 2x.
Q9. Log eˣ is named as logarithms ________
The natural logarithm is defined as the logarithm with base e, so log eˣ simplifies to x and is referred to as the natural logarithm.
Q10. d/dx (aˣ) =
The derivative of aˣ with respect to x is aˣ multiplied by the natural logarithm of the base a, a standard result from exponential differentiation.
Q11. d/dx (5x²) =
The derivative of 5x² is found using the power rule: multiply the exponent by the coefficient and reduce the exponent by one, yielding 10x.
Q12. d/dx (cot⁻¹ x) =
The derivative of cot⁻¹ x is -1/(1+x²), which is a standard inverse trigonometric derivative.
Q13. Which one is a chain rule:
The chain rule states that if y is a function of u and u is a function of x, then dy/dx = dy/du × du/dx.
Q14. d/dx (cos x) =
The derivative of cos x is -sin x by standard trigonometric differentiation rules.
Q15. d/dx (tan x) =
The derivative of tan x is sec²x, a standard result in differential calculus.
Q16. d/dx (x⁴ + 1) =
The derivative of x⁴ is 4x³ by the power rule, and the derivative of the constant 1 is zero, so the result is 4x³.
Q17. d/dx (xⁿ) = n xⁿ⁻¹ is a rule ______
The power rule states that the derivative of x raised to a power n is n times x raised to n minus one, which matches the given expression exactly.
Q18. Derivative of any constant term is:
The derivative measures the rate of change, and a constant has no variation with respect to the variable. Thus, its derivative is always zero.
Q19. The notation 'f(x)' for a function was popularized by:
Euler introduced the modern function notation f(x), while Leibniz developed differential notation.
Q20. y = f(x); the dependent variable is:
In the function y = f(x), y depends on the value of x, making y the dependent variable and x the independent variable.
Chapter 2: Differentiation Revision Guide
Complete the MCQs first, then review every incorrect answer against the textbook heading where that concept appears. For biology and other science subjects, pay attention to terminology, diagrams, sequence of processes, examples and differences between similar structures or functions.
This chapter page keeps the exact class, subject, chapter, question count, answer checking, explanations and follow-up chapters together, so students can revise from one focused URL instead of searching through the full book again.
class 12 Mathematics MCQ Preparation: Differentiation
This page supports Intermediate Part 2 practice in Mathematics. At this stage, the main purpose is consolidating advanced concepts while balancing board revision, college assessments and admission preparation. The questions available here should be used with the current textbook and the instructions issued by the learner's school or examination board.
What Mathematics MCQs can test
In Mathematics, objective questions commonly draw on definitions, formulas, identities, properties, signs, graphs, theorem statements and short calculations. A useful answer is based on the exact wording and concept, not simply on recognising a familiar option. For this subject, learners should identify the rule being tested, perform the essential working separately and check signs, restrictions and units before selecting an option.
Differentiation: what to focus on
Notation, rules, derivatives, rates of change, limits, continuity, graphs and the conditions needed for a correct mathematical result.
Write the relevant rule first, show each algebraic step and check the domain or graph so that a familiar-looking option is not selected without verifying the calculation.
Common mistakes for class 12 learners
In this subject, frequent errors include sign mistakes, using a formula outside its conditions, confusing similar properties or selecting an answer from mental arithmetic without verification. Pay special attention to links between earlier intermediate concepts and the more advanced applications introduced in the final year. When the page marks an answer as incorrect, the next step should be to identify the mistaken idea and verify it, rather than memorising the displayed answer letter.
A practical revision routine
Use mixed recall and application questions, then revisit the chapters where formulas, processes or closely related terms are confused. Before attempting the MCQs, review formulas, identities, definitions, graph behavior, theorem conditions and representative solved examples. Complete a manageable set without notes, check the result, and divide errors into missing knowledge, misunderstood concepts and careless reading. Revise the appropriate section before repeating the chapter.
How to review Differentiation after the quiz
List the questions you missed from Differentiation and write the textbook heading connected with each one. Explain the correct idea in your own words, then return later and answer a fresh set. This gives the chapter page a clear purpose: finding specific weaknesses in Mathematics rather than only collecting a score.
Accuracy and responsible use
Explanations are provided where they exist in the question bank, but educational databases can contain incomplete or mistaken material. Confirm disputed answers with an authoritative textbook or teacher. Ahmad Learning Hub provides a practice resource and does not claim that a question will appear in an examination or that every available item represents an official board question.