IB Class 10 Mathematics – Group 5, Calculus | 3. Derivatives by Abraham | Learn Smarter
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3. Derivatives

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Sections

  • 1

    Concept Of The Derivative

    The derivative is a fundamental concept in calculus that measures how a function changes as its input changes.

    Learning Practice

  • 1.1

    What Is A Derivative?

    The derivative is a fundamental concept in calculus that measures the rate of change of a function.

    Learning Practice

  • 1.2

    Definition Of The Derivative (Limit Definition)

    The derivative at a point measures the rate of change of a function as its input changes, defined through the limit of the difference quotient.

    Learning Practice

  • 2

    Basic Rules Of Differentiation

    This section introduces the basic rules of differentiation, including the derivatives of constant functions, power functions, and the application of sum, difference, and constant multiple rules.

    Learning Practice

  • 2.1

    Derivative Of A Constant Function

    The derivative of a constant function is always zero as there is no rate of change.

    Learning Practice

  • 2.2

    Derivative Of Power Functions (Power Rule)

    This section introduces the Power Rule for finding the derivative of power functions, allowing for quick calculations and understanding of polynomial behavior.

    Learning Practice

  • 2.3

    Sum And Difference Rules

    The Sum and Difference rules provide a shortcut for finding the derivatives of functions that are expressed as the sum or difference of two other functions.

    Learning Practice

  • 2.4

    Constant Multiple Rule

    The Constant Multiple Rule allows students to differentiate functions that are multiplied by a constant, maintaining the relationship between the constant and the derivative of the function itself.

    Learning Practice

  • 3

    Common Derivatives

    This section focuses on common derivative functions and their calculation, vital for understanding calculus principles.

    Learning Practice

  • 4

    Finding The Equation Of A Tangent Line

    This section explains how to find the equation of a tangent line to a function using its derivative at any given point.

    Learning Practice

  • 5

    Applications Of Derivatives

    Derivatives play a crucial role in measuring rates of change and identifying maxima and minima of functions.

    Learning Practice

  • 5.1

    Rate Of Change

    The rate of change is a fundamental concept in calculus represented by derivatives, indicating how a function varies with respect to its input.

    Learning Practice

  • 5.2

    Finding Maximum And Minimum Values

    The section discusses how to find local maxima and minima of functions using derivatives.

    Learning Practice

  • 6

    Step-By-Step Examples

    This section provides step-by-step examples illustrating how to find derivatives and interpret the slope of tangent lines.

    Learning Practice

  • 7

    Summary

    The section provides a foundational understanding of derivatives, focusing on their definition, computation, and applications.

    Learning Practice

References

10 IB calculus ch3.pdf

Class Notes

Memorization

Revision Tests