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Unformatted text preview: wtm369 – Homework 6 – Helleloid – (58250) 1 This printout should have 17 questions. Multiplechoice 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 ) = 6 x cos2 x 8 sin2 x . 1. f ′ ( x ) = 16 cos2 x 10 x sin2 x 2. f ′ ( x ) = 12 x sin2 x 10 cos2 x 3. f ′ ( x ) = 16 cos2 x + 12 x sin2 x 4. f ′ ( x ) = 12 x sin2 x 16cos2 x 5. f ′ ( x ) = 12 x sin2 x 10 cos2 x correct Explanation: Using formulas for the derivatives of sine and cosine together with the Product and Chain Rules, we see that f ′ ( x ) = 6 cos2 x 12 x sin2 x 16cos2 x = 12 x sin2 x 10 cos2 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 2. f ′ ( x ) = 6( x 2) ( x + 1) 3 3. f ′ ( x ) = 6( x + 1) ( x 1) 3 4. f ′ ( x ) = 6( x + 2) ( x 1) 3 5. f ′ ( x ) = 4( x 1) ( x + 1) 3 correct 6. f ′ ( x ) = 4( x 2) ( 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 4 x . 1. f ′ ( x ) = x 2 (4 x x 2 ) 3 / 2 2. f ′ ( x ) = 2 x (4 x x 2 ) 3 / 2 3. f ′ ( x ) = 2 x ( x 2 4 x ) 3 / 2 correct 4. f ′ ( x ) = x 2 ( x 2 4 x ) 3 / 2 5. f ′ ( x ) = 2 x ( x 2 4 x ) 1 / 2 6. f ′ ( x ) = x 2 (4 x x 2 ) 1 / 2 Explanation: By the Chain Rule, f ′ ( x ) = 1 2( x 2 4 x ) 3 / 2 (2 x 4) . Consequently, f ′ ( x ) = 2 x ( x 2 4 x ) 3 / 2 . wtm369 – Homework 6 – Helleloid – (58250) 2 004 10.0 points Determine the derivative of f ( x ) = x √ 1 + x. 1. f ′ ( x ) = 2 3 x 2 √ 1 + x 2. f ′ ( x ) = 2 + 3 x 2 √ 1 + x correct 3. f ′ ( x ) = 1 + 2 x √ 1 + x 4. f ′ ( x ) = 1 2 x √ 1 + x Explanation: By the Product and Chain Rules, f ′ ( x ) = √ 1 + x + x 2 √ 1 + x = 2(1 + x ) + x 2 √ 1 + x Consequently, f ′ ( x ) = 2 + 3 x 2 √ 1 + x 005 10.0 points Find the derivative of y when y = 2 sin √ x 10 √ x cos √ x . 1. y ′ = cos √ x + 4 parenleftBig sin √ x √ x parenrightBig 2. y ′ = sin √ x + 4 parenleftBig cos √ x √ x parenrightBig 3. y ′ = sin √ x + 6 parenleftBig sin √ x √ x parenrightBig 4. y ′ = 5 sin √ x 6 parenleftBig cos √ x √ x parenrightBig 5. y ′ = 5 sin √ x 4 parenleftBig cos √ x √ x parenrightBig correct 6. y ′ = 5 cos √ x 6 parenleftBig sin √ x √ x parenrightBig Explanation: By the Product and Chain Rules,...
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This note was uploaded on 12/04/2009 for the course M 408k taught by Professor Schultz during the Fall '08 term at University of Texas.
 Fall '08
 schultz
 Calculus

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