1 / 10

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:.

haru
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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.

More Related