Exam 3: Shortcuts to Differentiation

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Given Given   ,   , and   , find   . Enter fractions in the form a/b. , Given   ,   , and   , find   . Enter fractions in the form a/b. , and Given   ,   , and   , find   . Enter fractions in the form a/b. , find Given   ,   , and   , find   . Enter fractions in the form a/b. . Enter fractions in the form "a/b".

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Find Find   for   . for Find   for   . .

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The cost to produce q aircraft in South Africa is given by the function The cost to produce q aircraft in South Africa is given by the function   , with C in millions of rands. At a production level of 60 aircraft, how many million rands will it cost to produce one more aircraft? Round to 2 decimal places. , with C in millions of rands. At a production level of 60 aircraft, how many million rands will it cost to produce one more aircraft? Round to 2 decimal places.

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Given Given   ,   , and   , find   . , Given   ,   , and   , find   . , and Given   ,   , and   , find   . , find Given   ,   , and   , find   . .

(Multiple Choice)
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Find the derivative of Find the derivative of

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Find the derivative of Find the derivative of   . .

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Compute Compute   for   . for Compute   for   . .

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Consider the function Consider the function   , where a and b are constants. Find   . , where a and b are constants. Find Consider the function   , where a and b are constants. Find   . .

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Find the derivative of Find the derivative of   . .

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Find the derivative of Find the derivative of   . .

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Find the first derivative of Find the first derivative of

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Find and simplify the derivative of Find and simplify the derivative of   . .

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Find the derivative of Find the derivative of   . .

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The number of hours, H, of daylight in Madrid as a function of the date is given by the formula The number of hours, H, of daylight in Madrid as a function of the date is given by the formula   , where t is the number of days since the beginning of the year. What is   ? Round to 3 decimal places. , where t is the number of days since the beginning of the year. What is The number of hours, H, of daylight in Madrid as a function of the date is given by the formula   , where t is the number of days since the beginning of the year. What is   ? Round to 3 decimal places. ? Round to 3 decimal places.

(Short Answer)
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The derivative of The derivative of   is   . is The derivative of   is   . .

(True/False)
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The height off the ground of a person riding a Ferris wheel is represented by the function The height off the ground of a person riding a Ferris wheel is represented by the function   . On which interval(s) is   increasing? . On which interval(s) is The height off the ground of a person riding a Ferris wheel is represented by the function   . On which interval(s) is   increasing? increasing?

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Find Find   if   . if Find   if   . .

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The concentration, in The concentration, in   , of a drug introduced gradually into the body can be modeled by   . What is the rate of change in the concentration at t = 120? , of a drug introduced gradually into the body can be modeled by The concentration, in   , of a drug introduced gradually into the body can be modeled by   . What is the rate of change in the concentration at t = 120? . What is the rate of change in the concentration at t = 120?

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The first derivative of The first derivative of   is   . is The first derivative of   is   . .

(True/False)
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A tomato is thrown from the top of a tomato cart its distance from the ground, in feet, is modeled by the equation A tomato is thrown from the top of a tomato cart its distance from the ground, in feet, is modeled by the equation   where t is measured in seconds and the initial height of the cart is   feet. (A) At what time is the tomato at its maximum height? (B) What is the maximum height? (C) What is the initial velocity of the tomato (at t = 0)? where t is measured in seconds and the initial height of the cart is A tomato is thrown from the top of a tomato cart its distance from the ground, in feet, is modeled by the equation   where t is measured in seconds and the initial height of the cart is   feet. (A) At what time is the tomato at its maximum height? (B) What is the maximum height? (C) What is the initial velocity of the tomato (at t = 0)? feet. (A) At what time is the tomato at its maximum height? (B) What is the maximum height? (C) What is the initial velocity of the tomato (at t = 0)?

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