Homework #6 - jiwani (amj566) – Homework06 – Fouli –...

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Unformatted text preview: jiwani (amj566) – Homework06 – Fouli – (58395) 1 This print-out should have 16 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 when f ( x ) = 4 x cos 3 x- 2 sin 3 x . 1. f ′ ( x ) =- 6 cos 3 x + 12 x sin 3 x 2. f ′ ( x ) = 12 x sin 3 x- 2 cos3 x 3. f ′ ( x ) = 6 cos 3 x- 2 x sin 3 x 4. f ′ ( x ) =- 12 x sin3 x- 2 cos 3 x correct 5. f ′ ( x ) =- 12 x sin3 x- 6 cos3 x Explanation: Using formulas for the derivatives of sine and cosine together with the Product and Chain Rules, we see that f ′ ( x ) = 4 cos 3 x- 12 x sin3 x- 6 cos3 x =- 12 x sin 3 x- 2 cos 3 x . 002 10.0 points Determine f ′ ( x ) when f ( x ) = x- 1 √ x 2- 2 . 1. f ′ ( x ) = 2 + x ( x 2- 2) 3 / 2 2. f ′ ( x ) = x- 2 ( x 2- 2) 1 / 2 3. f ′ ( x ) = 2- x ( x 2- 2) 3 / 2 4. f ′ ( x ) = x- 2 ( x 2- 2) 3 / 2 correct 5. f ′ ( x ) = x + 2 ( x 2- 2) 1 / 2 6. f ′ ( x ) = 2- x ( x 2- 2) 1 / 2 Explanation: By the Product and Chain Rules, f ′ ( x ) = 1 ( x 2- 2) 1 / 2- 2 x ( x- 1) 2( x 2- 2) 3 / 2 = ( x 2- 2)- x ( x- 1) ( x 2- 2) 3 / 2 . Consequently, f ′ ( x ) = x- 2 ( x 2- 2) 3 / 2 . (Note: the Quotient Rule could have been used, but it’s simpler to use the Product Rule.) 003 10.0 points Find the derivative of y when y = 6 sin √ x- 8 √ x cos √ x . 1. y ′ = 4 sin √ x- cos √ x √ x correct 2. y ′ = 4 cos √ x- 7 parenleftBig sin √ x √ x parenrightBig 3. y ′ = 4 sin √ x- 7 parenleftBig cos √ x √ x parenrightBig 4. y ′ = 3 sin √ x + cos √ x √ x 5. y ′ = 3 sin √ x + 7 parenleftBig sin √ x √ x parenrightBig 6. y ′ = 3 cos √ x + sin √ x √ x Explanation: jiwani (amj566) – Homework06 – Fouli – (58395) 2 By the Product and Chain Rules, y ′ = 3 parenleftBig cos √ x √ x parenrightBig- 4 parenleftBig cos √ x √ x parenrightBig + 4 parenleftBig √ x sin √ x √ x parenrightBig . Consequently, y ′ = 4 sin √ x- cos √ x √ x . 004 10.0 points Find the derivative of f when f ( x ) = parenleftBig 4 x 3 / 2- x − 3 / 2 parenrightBig 2 . 1. f ′ ( x ) = 4 parenleftbigg 16 x 6 + 1 x 4 parenrightbigg 2. f ′ ( x ) = 3 parenleftbigg 4 x 3 + 1 x 3 parenrightbigg 3. f ′ ( x ) = 4 parenleftbigg 16 + x − 6 x 3 parenrightbigg 4. f ′ ( x ) = 3 parenleftbigg 4 x 6- 1 x 3 parenrightbigg 5. f ′ ( x ) = 3 parenleftbigg 16 x 6- 1 x 4 parenrightbigg correct 6. f ′ ( x ) = 4 parenleftbigg 16- x − 6 x...
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This note was uploaded on 07/10/2011 for the course KIN 321M taught by Professor Jensen during the Spring '11 term at University of Texas.

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Homework #6 - jiwani (amj566) – Homework06 – Fouli –...

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