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HW06-solutions - vasquez(mpv244 HW06 Schultz(56445 This...

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vasquez (mpv244) – HW06 – Schultz – (56445) 1 This print-out should have 15 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 6 x. 1. f ( x ) = 4 cos 4 x - 4 x sin 6 x 2. f ( x ) = 4 cos 6 x - 24 x sin 6 x correct 3. f ( x ) = 24 cos 6 x + 6 x sin 6 x 4. f ( x ) = 24 cos 6 x - 4 x sin 6 x 5. f ( x ) = 4 cos 6 x + 24 x sin 4 x Explanation: Using the formulas for the derivatives of sine and cosine together with the Chain Rule we see that f ( x ) = (4 x ) cos 6 x + 4 x (cos 6 x ) = 4 cos 6 x - 24 x sin 6 x. 002 10.0 points Determine the derivative of f ( x ) = ( x + 2) x + 1 . 1. f ( x ) = 3 x + 4 2 x + 1 correct 2. f ( x ) = 3 x - 4 x + 1 3. f ( x ) = 3 x - 4 2( x + 1) 4. f ( x ) = 3 x + 4 x + 1 5. f ( x ) = 3 x - 4 x + 1 6. f ( x ) = 3 x + 4 2( x + 1) Explanation: By the Product and Chain Rules, f ( x ) = 1 2 x + 1 ( x + 2) + x + 1 = x + 2 + 2( x + 1) 2 x + 1 . Consequently, f ( x ) = 3 x + 4 2 x + 1 . keywords: Product Rule, Chain Rule, Power Rule, square root function, 003 10.0 points Determine f ( x ) when f ( x ) = 2 cos 2 x - 3 sin 2 x. 1. f ( x ) = - 4 sin x - 6 cos x 2. f ( x ) = - 4 sin x + 6 cos x 3. f ( x ) = - 2 sin x cos x 4. f ( x ) = 10 sin x cos x 5. f ( x ) = 4 cos x + 6 sin x 6. f ( x ) = - 10 sin x cos x correct 7. f ( x ) = 2 sin x cos x Explanation: Since d dx sin x = cos x, d dx cos x = - sin x, the Chain Rule ensures that f ( x ) = - 4 cos x sin x - 6 sin x cos x.
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vasquez (mpv244) – HW06 – Schultz – (56445) 2 Consequently, f ( x ) = - 10 sin x cos x . 004 10.0 points Find the derivative of y when y = 4 sin x - 2 x cos x. 1. y = cos x + 3 parenleftBig sin x x parenrightBig 2. y = sin x - 3 parenleftBig cos x x parenrightBig 3. y = 2 sin x - cos x x 4. y = 2 cos x - sin x x 5. y = 2 sin x + 3 parenleftBig sin x x parenrightBig 6. y = sin x + cos x x correct Explanation: By the Product and Chain Rules, y = 2 parenleftBig cos x x
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