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Concept Maps

Differentiation — Concept Maps

ICSE · Class 12 · Mathematics

4 concept maps of Differentiation for ICSE Class 12 Mathematics, each also written out as a text outline. Part of the ICSE Class 12 Mathematics syllabus.

103 questions34 flashcards20 formulas & key relations5 concepts

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A flowchart or diagram explaining the step-by-step application of the chain rule for differentiating composite functions.
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4 Concept Maps

Complete Differentiation Techniques Overview

Complete Differentiation Techniques Overview

The map in words

  • Differentiation
    • Basic Rules
      • Power Rule
        • d/dx of x to n = nx to n minus 1
      • Exponential
        • d/dx of e to x = e to x
        • d/dx of a to x = a to x times log a
      • Logarithm
        • d/dx of log x = 1/x
      • Trig Functions
        • sin x to cos x
        • cos x to negative sin x
        • tan x to sec squared x
    • Chain Rule
      • Composite Functions
        • Outer function derivative
        • Times inner function derivative
      • Nested Functions
        • Three or more layers
        • Apply repeatedly outside to inside
    • Product and Quotient
      • Product Rule
        • u times dv plus v times du
      • Quotient Rule
        • Low d High minus High d Low
        • All over Low Squared
    • Implicit Differentiation
      • Both sides w.r.t. x
      • Each y term gets dy/dx factor
      • Collect and solve for dy/dx
      • Infinite expressions
        • Self similar structure
        • Simplify first
    • Logarithmic Differentiation
      • f of x to power g of x
      • Take log both sides
      • Differentiate
      • Multiply by y
    • Inverse Trig Derivatives
      • sin inverse = 1 over root 1 minus x squared
      • cos inverse = negative 1 over root 1 minus x squared
      • tan inverse = 1 over 1 plus x squared
      • Simplify before differentiating
    • Parametric Forms
      • dy/dx = dy/dt divided by dx/dt
      • Second derivative uses chain rule
    • Second Order Derivatives
      • Differentiate first derivative again
      • Standard results y double prime plus n squared y = 0

Flowchart showing the concept of differentiation from function to rate of change interpretation

Flowchart showing the concept of differentiation from function to rate of change interpretation

The map in words

  • Function f(x)
    • Apply Differentiation: Derivative f'(x)
      • Interpretation: Rate of Change
        • At specific point: Instantaneous slope
          • Geometric meaning: Slope of tangent line
            • Applications: Velocity, Acceleration, Optimization

Mind map showing the hierarchy of basic differentiation rules

Mind map showing the hierarchy of basic differentiation rules

The map in words

  • Basic Rules
    • Constant Rule
      • d/dx(c) = 0
      • Any constant vanishes
    • Power Rule
      • d/dx(xⁿ) = nxⁿ⁻¹
      • Bring down exponent
      • Reduce exponent by 1
    • Sum/Difference
      • Differentiate each term
      • Combine results
    • Constant Multiple
      • Pull constant outside
      • Differentiate function

Differentiation as the study of finding derivatives of functions and using them through basic rules, chain rule, implicit differentiation, logarithmic differentiation, inverse trigonometric differentiation, parametric form, derivative w.r.t. another function, and determinants

Differentiation as the study of finding derivatives of functions and using them through basic rules, chain rule, implicit differentiation, logarithmic differentiation, inverse trigonometric differentiation, parametric form, derivative w.r.t. another function, and determinants

The map in words

  • Differentiation as the study of finding derivatives of functions and using them through basic rules, chain rule, implicit differentiation, logarithmic differentiation, inverse trigonometric differentiation, parametric form, derivative w.r.t. another function, and determinants
    • Derivative
    • First Principle method
    • Basic differentiation rules
    • Exponential and logarithmic derivatives
    • Chain Rule
    • Trigonometric differentiation
    • Implicit differentiation
    • Second order derivative

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Frequently Asked Questions

What are the important topics in Differentiation for ICSE Class 12 Mathematics?
Key topics in Differentiation include Core idea of derivative and first principle, Basic derivative rules and standard formulas, Implicit differentiation and related working rule, Second order derivatives. Study these first, then practise questions on each for the ICSE Class 12 board exam.
What do the concept maps for Differentiation show?
The 4 maps show how the ideas in Differentiation connect: Complete Differentiation Techniques Overview; Flowchart showing the concept of differentiation from function to rate of change interpretation. Each map is also written out as an outline on this page.
How should I revise Differentiation for the ICSE Class 12 board exam?
Learn the core ideas first, then work through the 103 practice questions on Differentiation. 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 Differentiation

All ICSE Class 12 Mathematics Concept Maps

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