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Differentiation

Maharashtra Board · Class 12 · Mathematics & Statistics -Commerce

Practice quiz for Differentiation — Maharashtra Board Class 12 Mathematics & Statistics -Commerce. MCQs and questions with answers to test your preparation.

42 questions20 flashcards5 concepts

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Quick Quiz: Differentiation

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1

Find dy/dx if y = (3x² + 2x - 1)⁵

2

If y = log(2x³ - 5x + 1), find dy/dx

3

Find dy/dx if y = e^(3x² + 2x)

4

If y = 15 + 8x + 2x², find dx/dy (rate of change of demand with respect to price)

42 Questions·
multiple choicemultiple correct

Sample Questions

1multiple correct

Which of the following are correct for logarithmic differentiation? (Select all correct)

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For y = x^x, take log of both sides first, d/dx(log y) = (1/y) × (dy/dx), For y = f(x)^g(x), use logarithmic differentiation, log(m/n) = log m - log n

Logarithmic differentiation is used when the variable appears in both base and exponent. The key formula is d/dx(log y) = (1/y) × (dy/dx). Also, log(m/n) = log m - log n, but log(mn) = log m + log n, not multiplication.

2multiple choice

Find dy/dx if x² + y² = 25

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-x/y

For implicit differentiation of x² + y² = 25: Differentiate both sides with respect to x: 2x + 2y(dy/dx) = 0. Solving for dy/dx: 2y(dy/dx) = -2x, therefore dy/dx = -x/y

3multiple choice

If x = 3t², y = 6t, find dy/dx

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1/t

For parametric functions: dx/dt = 6t and dy/dt = 6. Using the formula dy/dx = (dy/dt)/(dx/dt) = 6/(6t) = 1/t

4multiple choice

Find d²y/dx² if y = x⁴

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12x²

First derivative: dy/dx = 4x³. Second derivative: d²y/dx² = d/dx(4x³) = 12x². This is the second-order derivative of the given function.

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Frequently Asked Questions

What are the important topics in Differentiation for Maharashtra Board Class 12 Mathematics & Statistics -Commerce?
Differentiation covers several key topics that are frequently asked in Maharashtra Board Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Differentiation — Maharashtra Board Class 12 Mathematics & Statistics -Commerce?
Understand the core concepts first, then work through the 42 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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