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Solutions HW 6

Solutions HW 6 - mao(tm23477 – Hw6 – gualdani –(57180...

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Unformatted text preview: mao (tm23477) – Hw6 – gualdani – (57180) 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Determine f ′ ( x ) when f ( x ) = 2 sec 2 x- 3 tan 2 x . 1. f ′ ( x ) =- 2 tan 2 sec x 2. f ′ ( x ) = 2 tan 2 sec x 3. f ′ ( x ) = 10 sec 2 x tan x 4. f ′ ( x ) = 10 tan 2 sec x 5. f ′ ( x ) = 2 sec 2 x tan x 6. f ′ ( x ) =- 2 sec 2 x tan x correct Explanation: Since d dx sec x = sec x tan x, d dx tan x = sec 2 x, the Chain Rule ensures that f ′ ( x ) = 4 sec 2 x tan x- 6 tan x sec 2 x . Consequently, f ′ ( x ) =- 2 sec 2 x tan x . 002 10.0 points Find the derivative of f when f ( x ) = 6 x 2 (4- sin x ) 5 . 1. 12 x (4- sin x ) 5 parenleftBig 8- 2 sin x- 5 cos x parenrightBig 2. 12 x (4- sin x ) 4 parenleftBig 8- 2 sin x- 5 cos x parenrightBig 3. 6 x (4- sin x ) 4 parenleftBig 8- 2 sin x + 5 x cos x parenrightBig 4. 6 x (4- sin x ) 5 parenleftBig 8- 5 x cos x parenrightBig 5. 6 x (4- sin x ) 4 parenleftBig 8- 2 sin x- 5 x cos x parenrightBig correct Explanation: By the Product rule f ′ ( x ) = 12 x (4- sin x ) 5 +6 x 2 d dx (4- sin x ) 5 . But the Power rule ensures that d dx (4- sin x ) 5 =- 5(4- sin x ) 4 cos x. Consequently, f ′ ( x ) = 6 x (4- sin x ) 4 braceleftBig 2(4- sin x )- 5 x cos x bracerightBig = 6 x (4- sin x ) 4 parenleftBig 8- 2 sin x- 5 x cos x parenrightBig . 003 10.0 points Find the derivative of f when f ( x ) = 3 x cos 5 x . 1. f ′ ( x ) = 3 cos5 x- 15 x sin 5 x correct 2. f ′ ( x ) = 3 cos5 x + 15 x sin 3 x 3. f ′ ( x ) = 15cos 5 x + 5 x sin 5 x 4. f ′ ( x ) = 3 cos3 x- 3 x sin5 x 5. f ′ ( x ) = 15cos 5 x- 3 x sin 5 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 5 x + 3 x (cos 5 x ) ′ = 3 cos5 x- 15 x sin 5 x . mao (tm23477) – Hw6 – gualdani – (57180) 2 004 10.0 points Find the derivative of f when f ( x ) = cos(cos x ) . 1. f ′ ( x ) = sin x sin(sin x ) 2. f ′ ( x ) = cos x sin(cos x ) 3. f ′ ( x ) =- cos x sin(cos x ) 4. f ′ ( x ) = sin x sin(cos x ) correct 5. f ′ ( x ) =- sin x sin(cos x ) 6. f ′ ( x ) =- cos x sin(sin x ) Explanation: Using the Chain Rule we see that f ′ ( x ) = parenleftBig- sin(cos x ) parenrightBig (- sin x ) = sin x sin(cos x ) ....
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Solutions HW 6 - mao(tm23477 – Hw6 – gualdani –(57180...

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