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2.2 Differentiation Rules for Constant Multiples, Sums, Powers, Sines, and Cosines

2.2 Differentiation Rules for Constant Multiples, Sums, Powers, Sines, and Cosines. Constant Rule:. The derivative of a constant is zero. Find the derivatives of:. Power Rule:. If n is a rational number, then. Find the derivatives of:. rewritten as. Differentiate:.

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2.2 Differentiation Rules for Constant Multiples, Sums, Powers, Sines, and Cosines

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  1. 2.2 Differentiation Rules for Constant Multiples, Sums, Powers, Sines, and Cosines Constant Rule: The derivative of a constant is zero. Find the derivatives of:

  2. Power Rule: If n is a rational number, then Find the derivatives of: rewritten as

  3. Differentiate: Sum and Difference Rules

  4. Differentiate: Derivatives of Sine and Cosine

  5. Find the slope and equation of the tangent line of the graph of y = 2 cos x at the point f’(x) = -2sin x Therefore, the equation of the tangent line is: Day 1

  6. The average rate of change in distance with respect to time is given by… change in distance change in time Also known as average velocity

  7. Ex. If a free-falling object is dropped from a height of 100 feet, its height s at time t is given by the position function s = -16t2 + 100, where s is measured in feet and t is measured in seconds. Find the average rate of change of the height over the following intervals. a. [1, 2] b. [1, 1.5] c. [1, 1.1] a. b. c.

  8. At time t = 0, a diver jumps from a diving board that is 32 feet above the water. The position of the diver is given by where s is measured in feet and t in seconds. • When does the diver hit the water? • What is the diver’s velocity at impact? To find the time at which the diver hits the water, we let s(t) = 0 and solve for t. t = -1 or 2 -1 doesn’t make sense, so the diver hits at 2 seconds.

  9. The velocity at time t is given by the derivative. s’(t) = v(t) = -32t + 16 @ t = 2 seconds, s’(2) = -48 ft/sec. The negative gives the direction, which in this case is down.

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