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Grade 12

Mathematics

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Welcome!

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Differentiation

3-6: Derivatives of Trigonometric Functions

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Learning objectives

    • Find the derivatives trigonometric functions using differentiation rules.
    • Solve physical and engineering problems using derivatives of trigonometric functions.

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Keywords

  • Derivates of Trigonometric Functions

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  • Spring Mass Systems

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Prerequisite

  • Power Rule

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  • Product Rule

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  • Quotient Rule

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  • Chain Rule

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The Derivatives of the Six Trigonometric Functions

 

 

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Example 1�A Derivative the Requires the Product Rule

 

 

 

Product Rule

 

 

 

 

 

 

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Student Task 1

 

 

 

Product Rule

 

 

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Example 2�Computing Some Routine Derivatives

Compute the derivative of:

 

 

 

 

 

 

 

 

 

 

 

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Example 2�Computing Some Routine Derivatives

Compute the derivative of:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Student Task 2

 

 

Compute the derivative of:

 

 

 

 

 

 

 

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Example 3�The Derivatives of Some Similar Trigonometric Functions

Compute the derivative of:

 

 

 

 

 

 

 

 

 

 

 

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Example 3�The Derivatives of Some Similar Trigonometric Functions

Compute the derivative of:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Example 3�The Derivatives of Some Similar Trigonometric Functions

Compute the derivative of:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Student Task 3

 

 

 

 

Compute the derivative of:

 

 

 

 

 

 

 

 

 

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Example 4�A Derivative Involving the Chain Rule and the Quotient Rule

 

 

 

 

 

 

 

 

 

 

Quotient Rule

 

 

 

 

 

 

 

 

 

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Student Task 4

 

 

 

 

 

Quotient Rule

 

 

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Example 5�Analysis of a Spring Mass System

 

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Example 5�Analysis of a Spring Mass System

 

 

 

 

 

 

 

 

 

 

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Student Task 5

 

 

 

 

 

 

 

 

 

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Summary

Derivates of Trigonometric Functions

 

 

 

Quotient Rule

Power Rule

 

 

Product Rule

 

Chain Rule

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