1 / 10

4-3 Derivative of a Quotient of Two Functions

4-3 Derivative of a Quotient of Two Functions. Pages 136- 141 Katie Warmbold Jillian Defrietas. Introduction. This chapter allows you to solve “catching up problems” in which one moving object wants to reach another moving object. Topics of Discussion.

zander
Download Presentation

4-3 Derivative of a Quotient of Two Functions

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. 4-3Derivative of a Quotient of Two Functions Pages 136- 141 Katie Warmbold Jillian Defrietas

  2. Introduction • This chapter allows you to solve “catching up problems” in which one moving object wants to reach another moving object.

  3. Topics of Discussion • Property: Derivative of a Quotient of Two Functions: • If y = u/v, where u and v are differentiable functions, and v doesn’t equal 0, then u’v – uv’ y’ = v^2 Words – Derivative of top times bottom, minus top times derivative of bottom, all divided by bottom squared

  4. Relation to Earlier Lessons • In order to differentiate, or find the derivative, some functions, its important to remember the Property: Derivatives of Sine and Cosine Functions. • d/dx(sinx) = cosX • d/dx(cosx) = -sinX • The chain rule, explained in 3-7, is applied in numerous problems when finding the derivative.

  5. Typical Problem • Differentiate: (5x – 2)^7 y = (4x +9)^3 • Differentiate: d ( 5 ) dx ( 7x^3) • Differentiate: sin5x f(x) = 8x - 3

  6. Detailed Procedure • Problem # 1: (5x – 2)7 y= (4x +9)3 Use the Property to solve problem (HINT:Derivative of toptimesbottom, minustoptimesderivative of bottom, all divided bybottom squared.) The chain rule, as in 4-2, also is applied when finding derivatives y’ = 7(5x-2)^6(5) * (4x+9)^3 - (5x - 2)^7 * 3(4x + 9)^2(4) (4x + 9)^6 = (5x - 2)^6 (80x + 339) (4x + 9)^6

  7. Solution • Differentiate: • sin5x • f(x) = 8x - 3 • 1.) cos5x(5)(8x - 3) - sin5x(8) • f’x = (8x - 3)^2 • 2.) 5cos5x(8x - 3) - 8sin5x • f’x = (8x - 3)^2

  8. Real Life Example • Black Hole Problem : • Ann Astronaut’s spaceship gets trapped in the gravitational field of a black hole! Her velocity, v(t) miles per hour is given: • 1000 • v(t) = 3 - t • a.) How fast is she going when t=1? When t = 2? When t = 3? • B.) Write an equation for the acceleration function, a(t). • C.) What is her acceleration when t=1? When t = 2? When t = 3?

  9. Real Life Example Solution • A.) a(1) = 250 mph/hr • a(2) = 1000 mph/hr • a(3) = 1000/0 mph/hr = no answer • B.) 1000 • a(t) = (3 - t)^2 • C.) a(1) = 250 mph/hr • a(2) = 1000 mph/hr • a(3) = 1000/0 mph/hr = no answer

  10. Conclusion • This section taught you how to find an equation for the derivative function in one step when the function contains a quotient of two other functions. • The Property; Derivative of a Quotient of Two Functions was discussed and applied.

More Related