Problem Set 06s

Problem Set 06s - Hung Nguyen Problem Set 06 Solution 3.3...

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Hung Nguyen Problem Set 06 Solution GE 207C 3.3 Derivatives of Trigonometric Functions 3.4 Chain Rule 1 1. Find the derivative of the function a. ) sin( ) ( 3 / 1 x x x f = Solution: ( ) ( ) ( ) x x x x x x x x x dx d x x dx d x x f x x x f sin 3 1 ) cos( 3 1 sin ) cos( sin sin ) ( ' ) sin( ) ( 3 / 2 3 / 1 3 / 2 3 / 1 3 / 1 3 / 1 3 / 1 + = Ο Π Ξ Μ Ν Λ + = + = = b. 3 / 1 3 1 ) tan( ) cos( ) ( x x x x x f + = Solution: ( ) ( ) 3 / 4 3 2 3 / 4 3 3 3 / 1 3 3 / 1 3 3 1 ) cos( ) sin( 3 ) ( ' 3 1 sin 3 sin 3 / 1 sin 1 cos sin cos 1 ) tan( ) cos( ) ( + = Ο Π Ξ Μ Ν Λ + + = + = + = + = x x x x x x f x x dx d x x d x x x x x x x x x x x x x x f c. 2 1 cos ) ( x x x f = Solution: f ( x ) = cos x 1 x 2 f '( x ) = d dx cos x ( ) 1 x 2 ( ) cos x d dx 1 x 2 " # $ % 1 x 2 ( ) 2 = sin x ( ) 1 x 2 cos x ( ) 1 2 1 x 2 ( ) 1/2 ( 2 x ) & ' ( ) * + 1 x 2 ( ) 2 = sin x ( ) 1 x 2 + x cos x ( ) 1 x 2 ( ) 1/2 ( ) 1 x 2 ( ) 2 = sin x 1 x 2 + x cos x 1 x 2 ( ) 1 x 2 d. ( ) x x x f = 1 1 ) ( 2 Solution: f ( x ) = 1 x ( ) 2 1 x f '( x ) = d dx 1 x ( ) 2 " # $ % & ' 1 x ( ) 1 x ( ) 2 d dx 1 x ( ) 1 x ( ) 2 = 2 1 x ( ) 1 2 x 1/2 ( ) * + , - 1 x ( ) 1 x ( ) 2 1 ( ) 1 x ( ) 2 = 1 x ( ) x 1/2 ( ) 1 x ( ) + 1 x ( ) 2 1 x ( ) 2 f '( x ) = 1 x ( ) x 1/2 ( ) 1 x ( ) + 1 x ( ) 2 1 x ( ) 2 =
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Problem Set 06s - Hung Nguyen Problem Set 06 Solution 3.3...

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