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Differentials and Partial Derivatives — Concept Maps

Tamil Nadu Board · Class 12 · Mathematics

3 concept maps of Differentials and Partial Derivatives for Tamil Nadu Board Class 12 Mathematics, each also written out as a text outline.

45 questions26 flashcards3 formulas & key relations5 concepts

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3 Concept Maps

Mind map showing the main topics and subtopics covered in the chapter

Mind map showing the main topics and subtopics covered in the chapter

The map in words

  • Differentials and Partial Derivatives
    • Linear Approximation
      • Tangent line
      • Function values
    • Differentials
      • One variable
      • Multiple variables
    • Partial Derivatives
      • Two variables
      • Three variables
      • Higher order
    • Applications
      • Chain rule
      • Homogeneous functions
      • Euler's theorem

Step-by-step process for finding and using linear approximation

Step-by-step process for finding and using linear approximation

The map in words

  • Given: Function f and point x₀
    • Step 1: Find f(x₀)
      • Step 2: Find f'(x₀)
        • Step 3: Form tangent line L(x) = f(x₀) + f'(x₀)(x-x₀)
          • Step 4: Use L(x) to approximate f(x) for x near x₀
            • Linear Approximation Complete

Worked example showing each step of the linear approximation process

Worked example showing each step of the linear approximation process

The map in words

  • Problem: √9.2
    • Choose x₀=9 Δx=0.2
      • Compute f9=3 f'9=1/6
        • L9.2 = 3 + 1/6·0.2 = 3.0333
          • Compare with actual: 3.03315
            • Error very small!

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Frequently Asked Questions

What are the important topics in Differentials and Partial Derivatives for Tamil Nadu Board Class 12 Mathematics?
Key topics in Differentials and Partial Derivatives include Linear Approximation and Differentials (Single Variable), Functions of Several Variables: Limits and Continuity, Partial Derivatives, Linear Approximation and Differentials (Multiple Variables). Study these first, then practise questions on each for the Tamil Nadu Board Class 12 board exam.
What do the concept maps for Differentials and Partial Derivatives show?
The 3 maps show how the ideas in Differentials and Partial Derivatives connect: Mind map showing the main topics and subtopics covered in the chapter; Step-by-step process for finding and using linear approximation. Each map is also written out as an outline on this page.
How should I revise Differentials and Partial Derivatives for the Tamil Nadu Board Class 12 board exam?
Learn the core ideas first, then work through the 45 practice questions on Differentials and Partial Derivatives. Revise 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.

More resources for Differentials and Partial Derivatives

All Tamil Nadu Board Class 12 Mathematics Concept Maps

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