Derivative of Trigonometric Functions: Examples and Rules
Explore the derivative rules and examples of trigonometric functions with Mr. Brwa Ahmed at Tishk International University. Understand how to find the derivative of various trigonometric functions through practical examples in Math II Lecture 3.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
Mathematics Lecture 3 / Derivative of Trig. Functions Spring Semester 2019 Instructor Instructor A. S. Brwa A. S. Brwa MSc . Structural Engineering MSc . Structural Engineering brwa.ahmed@ishik.edu.iq brwa.ahmed@ishik.edu.iq Faculty of Engineering Faculty of Engineering Tishk Tishk InternationalUniversity InternationalUniversity
Tishk International University Derivative of Trigonometric Functions The Six Rules of Derivative of Trigonometric Function 2 Mr. Brwa Ahmed: Faculty of Engineering Math II Lecture 3 Derivative of Trigonometric Functions
Tishk International University Derivative of Trigonometric Functions 3 Mr. Brwa Ahmed: Faculty of Engineering Math II Lecture 3 Derivative of Trigonometric Functions
Tishk International University Derivative of Trigonometric Functions Angle sum and difference identities 4 Mr. Brwa Ahmed: Faculty of Engineering Math II Lecture 3 Derivative of Trigonometric Functions
Tishk International University Derivative of Trigonometric Functions Example 1: find the derivative of the trig function 1 2 2 = + + ( ) f x 5sin sec tan 7 3 x x x x x 1 2 2 ( ) = + + 5cos sec tan x sec tan (1) 14 x f x x x x x x 5 Mr. Brwa Ahmed: Faculty of Engineering Math II Lecture 3 Derivative of Trigonometric Functions
Tishk International University Derivative of Trigonometric Functions Example 2: find the derivative of the trig function ? = sin2 ? ? = ?2 ? = sin? ?? ??= ?? ?? ?? ??= 2? cos? = 2sin? cos? 6 Mr. Brwa Ahmed: Faculty of Engineering Math II Lecture 3 Derivative of Trigonometric Functions
Tishk International University Derivative of Trigonometric Functions Example 3: find the derivative of the trig function ? = sin(?2) ? = ???? ? = ?2 ?? ??= ?? ?? ?? ??= cos? 2? = 2? ??? ?2 7 Mr. Brwa Ahmed: Faculty of Engineering Math II Lecture 3 Derivative of Trigonometric Functions
Tishk International University Derivative of Trigonometric Functions Example 4: find the derivative of the trig function ? = ?2sin? 8 Mr. Brwa Ahmed: Faculty of Engineering Math II Lecture 3 Derivative of Trigonometric Functions
Tishk International University Derivative of Trigonometric Functions Example 5: find the derivative of the trig function 9 Mr. Brwa Ahmed: Faculty of Engineering Math II Lecture 3 Derivative of Trigonometric Functions
Tishk International University Derivative of Trigonometric Functions Example 6: find the derivative of the trig function 10 Mr. Brwa Ahmed: Faculty of Engineering Math II Lecture 3 Derivative of Trigonometric Functions
Tishk International University Derivative of Trigonometric Functions Example 7: find the derivative of the trig function 11 Mr. Brwa Ahmed: Faculty of Engineering Math II Lecture 3 Derivative of Trigonometric Functions
Tishk International University Derivative of Trigonometric Functions Example 8: find the derivative of the trig function + 1 sin x + x x = ( ) f x cos d dx d dx + (1 sin ) + (1 sin ) + + ( cos ) ( cos ) x x x x x x ( ) = f x 2 + ( cos ) x x + + ( cos )(cos ) x (1 sin )(1 sin ) cos ) x x x x x ( ) = f x 12 2 + ( x Mr. Brwa Ahmed: Faculty of Engineering Math II Lecture 3 Derivative of Trigonometric Functions
Tishk International University Derivative of Trigonometric Functions Example 8: find the derivative of the trig function 2 2 2 2 + (1 sin + 1 sin + ( cos x cos ( x ) ) cos cos x + x x x x x x x ( ) = = f x 2 2 + cos ) ( cos ) x x cos cos ) x + x x ( ) = f x 2 ( x 13 Mr. Brwa Ahmed: Faculty of Engineering Math II Lecture 3 Derivative of Trigonometric Functions
THANKS I HOPE YOU HAVE ENJOYED MY CLASS
