ICSE Class 12 Mathematics | 3. Calculus by Abraham | Learn Smarter
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3. Calculus

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Sections

  • 3

    Calculus

    Calculus is the mathematical study of rates of change and accumulation, primarily focusing on differentiation in this chapter.

    Learning Practice

  • 3.1

    Differentiation - Basic Concepts

    Differentiation focuses on finding the derivative of functions to understand how they change.

    Learning Practice

  • 3.2

    Derivative Rules

    This section covers the fundamental rules for differentiating various types of functions.

    Learning Practice

  • 3.2.1

    Power Rule

    The Power Rule is a fundamental differentiation rule that allows for the easy calculation of the derivative of a function defined as a power of x.

    Learning Practice

  • 3.2.2

    Sum Rule

    The Sum Rule in calculus allows the differentiation of the sum of two functions by differentiating each one individually.

    Learning Practice

  • 3.2.3

    Product Rule

    The Product Rule is a fundamental differentiation principle in calculus that explains how to find the derivative of the product of two functions.

    Learning Practice

  • 3.2.4

    Quotient Rule

    The Quotient Rule is a fundamental principle in calculus used to differentiate a function that is the ratio of two other functions.

    Learning Practice

  • 3.2.5

    Chain Rule

    The Chain Rule is a vital differentiation technique used to compute the derivative of composite functions.

    Learning Practice

  • 3.3

    Derivatives Of Trigonometric Functions

    This section discusses the derivatives of fundamental trigonometric functions and their importance in calculus.

    Learning Practice

  • 3.4

    Derivatives Of Exponential And Logarithmic Functions

    This section focuses on the derivatives of exponential and logarithmic functions, which are vital for calculus applications.

    Learning Practice

  • 3.4.1

    Exponential Functions

    This section discusses exponential functions, their derivatives, and their significance in calculus.

    Learning Practice

  • 3.4.2

    Logarithmic Functions

    This section delves into derivatives of logarithmic functions, focusing on their definitions and key properties.

    Learning Practice

  • 3.5

    Higher Order Derivatives

    Higher-order derivatives measure the rate of change of rates of change, providing insight into the behavior and curvature of graphs.

    Learning Practice

  • 3.6

    Application Of Derivatives

    This section covers the practical applications of derivatives, including finding tangents, normals, and identifying maxima and minima of functions.

    Learning Practice

  • 3.6.1

    Tangents And Normals

    This section explores the concepts of tangents and normals in calculus, detailing their equations and significance.

    Learning Practice

  • 3.6.2

    Maxima And Minima

    This section discusses the concepts of local maxima and minima and how they can be determined using derivatives.

    Learning Practice

  • 3.6.3

    Optimization Problems

    Optimization problems utilize calculus concepts to find maximum or minimum values of functions given specific constraints.

    Learning Practice

References

12 maths ch3.pdf

Class Notes

Memorization

Revision Tests