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Differentiation — Revision Notes

ICSE · Class 11 · Mathematics

Differentiation revision notes for ICSE Class 11 Mathematics: 4 topics in quick points. Part of the ICSE Class 11 Mathematics syllabus.

60 questions32 flashcards21 formulas & key relations5 concepts

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A graph of a function y=f(x) with a tangent line at a point (x, y), illustrating dy/dx as the slope of the tangent.
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Key Topics to Revise

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1. Differentiability at a Point

  • A function is differentiable at a point when the derivative exists finitely there.
  • A function is differentiable at x = c if the right-hand and left-hand limits both exist finitely and are equal.
  • A function is non-differentiable at x = c if it is not differentiable at x = c.
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2. First Principle and Meaning of Derivative

  • The first principle defines derivative using a small increment h.
  • The derivative of a function at x is written as f'(x).
  • dy/dx is another notation for derivative of y with respect to x.
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3. Basic Rules of Differentiation

  • The derivative of a constant is 0.
  • The derivative of x^n is n x^(n-1).
  • The derivative rules for sum, difference, scalar multiple, product, power of function, and quotient are essential for fast calculation.
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4. Standard Derivatives and Special Results

  • The derivative of sin x is cos x.
  • The derivative of cos x is -sin x.
  • The derivative of tan x is sec^2 x.

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Full Notes

Key Concepts

A function f is differentiable atThe limit lim_(xFor a general point xA function is nonThe derivative dy/dx at x =

Frequently Asked Questions

What are the important topics in Differentiation for ICSE Class 11 Mathematics?
Key topics in Differentiation include Differentiability at a Point, First Principle and Meaning of Derivative, Basic Rules of Differentiation, Standard Derivatives and Special Results. Study these first, then practise questions on each for Class 11 exams.
How should I revise Differentiation for Class 11 exams?
Learn the core ideas first, then work through the 60 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.

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All ICSE Class 11 Mathematics Revision Notes

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