HW6 (solutions)

HW6 (solutions) - myers(nmm698 – HW06 – Hamrick...

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Unformatted text preview: myers (nmm698) – HW06 – Hamrick – (54868) 1 This print-out should have 17 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Find the derivative of f ( x ) = 3 x sin4 x + 3 4 cos 4 x . 1. f ′ ( x ) = 12 x cos 4 x correct 2. f ′ ( x ) =- 12 x cos4 x 3. f ′ ( x ) = 12 x cos 4 x- 6 sin4 x 4. f ′ ( x ) = 12 cos 4 x 5. f ′ ( x ) = 12 x cos 4 x + 6 sin4 x Explanation: Since d dx sin x = cos x, d dx cos x =- sin x, it follows that f ′ ( x ) = 3 sin4 x + 12 x cos 4 x- 3 sin4 x. Consequently, f ′ ( x ) = 12 x cos 4 x . 002 10.0 points Find f ′ ( x ) when f ( x ) = parenleftBig x + 1 x- 1 parenrightBig 2 . 1. f ′ ( x ) =- 4( x + 1) ( x- 1) 3 correct 2. f ′ ( x ) = 6( x- 2) ( x + 1) 3 3. f ′ ( x ) =- 6( x + 2) ( x- 1) 3 4. f ′ ( x ) = 6( x- 1) ( x + 1) 3 5. f ′ ( x ) =- 4( x + 2) ( x- 1) 3 6. f ′ ( x ) = 4( x- 1) ( x + 1) 3 Explanation: By the Chain and Quotient Rules, f ′ ( x ) = 2 parenleftBig x + 1 x- 1 parenrightBig ( x- 1)- ( x + 1) ( x- 1) 2 . Consequently, f ′ ( x ) =- 4( x + 1) ( x- 1) 3 . 003 10.0 points Find f ′ ( x ) when f ( x ) = 1 √ x 2- 8 x . 1. f ′ ( x ) = 4- x ( x 2- 8 x ) 3 / 2 correct 2. f ′ ( x ) = x- 4 ( x 2- 8 x ) 3 / 2 3. f ′ ( x ) = 4- x ( x 2- 8 x ) 1 / 2 4. f ′ ( x ) = 4- x (8 x- x 2 ) 3 / 2 5. f ′ ( x ) = x- 4 (8 x- x 2 ) 3 / 2 6. f ′ ( x ) = x- 4 (8 x- x 2 ) 1 / 2 Explanation: By the Chain Rule, f ′ ( x ) =- 1 2( x 2- 8 x ) 3 / 2 (2 x- 8) . myers (nmm698) – HW06 – Hamrick – (54868) 2 Consequently, f ′ ( x ) = 4- x ( x 2- 8 x ) 3 / 2 . 004 10.0 points Find f ′ ( x ) when f ( x ) = 3 cos2 x + 2 cos 2 x . 1. f ′ ( x ) =- 8 cos 2 x 2. f ′ ( x ) = 16 cos 2 x 3. f ′ ( x ) =- 16 cos 2 x 4. f ′ ( x ) =- 16 sin2 x 5. f ′ ( x ) =- 8 sin2 x correct 6. f ′ ( x ) = 8 sin2 x Explanation: Differentiating once we see that f ′ ( x ) =- 6 sin2 x- 4 sin x cos x . Now 2 sin x cos x = sin2 x . Consequently, f ′ ( x ) =- 8 sin2 x . 005 10.0 points Find the derivative of f when f ( x ) = cos(cos x ) . 1. f ′ ( x ) =- cos x sin(cos x ) 2. f ′ ( x ) = cos x sin(cos x ) 3. f ′ ( x ) = sin x sin(cos x ) correct 4. f ′ ( x ) =- sin x sin(cos x ) 5. f ′ ( x ) =- cos x sin(sin x ) 6. f ′ ( x ) = sin x sin(sin x ) Explanation: Using the Chain Rule we see that...
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This note was uploaded on 03/10/2011 for the course M 408k taught by Professor Schultz during the Fall '08 term at University of Texas.

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HW6 (solutions) - myers(nmm698 – HW06 – Hamrick...

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