1205-hwt0305-slides

1205-hwt0305-slides - Outline Examples with Trigonometric...

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Unformatted text preview: Outline Examples with Trigonometric Derivatives Math 1205 3.5: The Chain Rule Heath David Hart Fall 2007 Heath David Hart Math 1205 3.5: The Chain Rule Outline Examples with Trigonometric Derivatives Table of Contents: Notes for Day 12: 3.5: The Chain Rule Examples with the Power Rule with the Exponential Rule with the Ln Rule with Trigonometric Derivatives Heath David Hart Math 1205 3.5: The Chain Rule Outline Examples with Trigonometric Derivatives Introduction Formally, the Chain Rule does for , what the Product Rule does for and the Quotient Rule does for : d dx f ( x ) g ( x ) = ( f ( x ) g ( x )) g ( x ) Heath David Hart Math 1205 3.5: The Chain Rule Outline Examples with Trigonometric Derivatives Example 1 If f ( x ) = sin x and g ( x ) = 13 x 2 , find the derivative of f ( x ) g ( x ): Heath David Hart Math 1205 3.5: The Chain Rule Outline Examples with Trigonometric Derivatives Example 1 If f ( x ) = sin x and g ( x ) = 13 x 2 , find the derivative of f ( x ) g ( x ): Solution: Using the Chain Rule: d dx f ( x ) g ( x ) = ( f ( x ) g ( x )) g ( x ) we get: d dx f ( x ) g ( x ) = ( cos x 13 x 2 ) 26 x Heath David Hart Math 1205 3.5: The Chain Rule Outline Examples with Trigonometric Derivatives Example 1 If f ( x ) = sin x and g ( x ) = 13 x 2 , find the derivative of f ( x ) g ( x ): If we write out the compositions on both sides, we get: d dx sin(13 x 2 ) = cos(13 x 2 ) 26 x ....
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This note was uploaded on 03/31/2008 for the course MATH 1205 taught by Professor Fbhinkelmann during the Fall '08 term at Virginia Tech.

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1205-hwt0305-slides - Outline Examples with Trigonometric...

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