# calc6 - pokharel(yp624 – HW06 – Radin –(56520 1 This...

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Unformatted text preview: pokharel (yp624) – HW06 – Radin – (56520) 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 ) = 3 x cos6 x . 1. f ′ ( x ) = 18 cos 6 x- 3 x sin6 x 2. f ′ ( x ) = 3 cos 3 x- 3 x sin 6 x 3. f ′ ( x ) = 3 cos 6 x- 18 x sin6 x correct 4. f ′ ( x ) = 3 cos 6 x + 18 x sin3 x 5. f ′ ( x ) = 18 cos 6 x + 6 x sin6 x Explanation: Using the formulas for the derivatives of sine and cosine together with the Chain Rule we see that f ′ ( x ) = (3 x ) ′ cos 6 x + 3 x (cos 6 x ) ′ = 3 cos 6 x- 18 x sin6 x . 002 10.0 points Determine the derivative of f ( x ) = ( x + 1) √ x + 2 . 1. f ′ ( x ) = 3 x + 5 2 √ x + 2 correct 2. f ′ ( x ) = 3 x + 5 √ x + 2 3. f ′ ( x ) = 3 x- 5 √ x + 2 4. f ′ ( x ) = 3 x + 5 2( x + 2) 5. f ′ ( x ) = 3 x- 5 x + 2 6. f ′ ( x ) = 3 x- 5 2( x + 2) Explanation: By the Product and Chain Rules, f ′ ( x ) = 1 2 √ x + 2 ( x + 1) + √ x + 2 = x + 1 + 2( x + 2) 2 √ x + 2 . Consequently, f ′ ( x ) = 3 x + 5 2 √ x + 2 . keywords: Product Rule, Chain Rule, Power Rule, square root function, 003 10.0 points Determine f ′ ( x ) when f ( x ) = 3 cos 2 x- 2 sin 2 x . 1. f ′ ( x ) = 2 sin x cos x 2. f ′ ( x ) =- 6 sin x + 4 cos x 3. f ′ ( x ) = 6 cos x + 4 sin x 4. f ′ ( x ) =- 10 sin x cos x correct 5. f ′ ( x ) = 10 sin x cos x 6. f ′ ( x ) =- 6 sin x- 4 cos x 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 ) =- 6 cos x sin x- 4 sin x cos x . pokharel (yp624) – HW06 – Radin – (56520) 2 Consequently, f ′ ( x ) =- 10 sin x cos x . 004 10.0 points Find the derivative of y when y = 6 sin √ x- 2 √ 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 ′ = 3 sin √ x + 4 parenleftBig sin √ x √ x parenrightBig 4. y ′ = sin √ x + 2 parenleftBig cos √...
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calc6 - pokharel(yp624 – HW06 – Radin –(56520 1 This...

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