1 / 18

Warm Up:

Warm Up:. h(x) is a composite function of f(x) and g(x) . Find f(x) and g(x) . 1. 2. THE CHAIN RULE. Objective: To use the chain rule to find the derivative of composite functions. What if we wanted to take the derivative of the following:. y=(2x+5) 2 y=(2x+5) 3 y=(2x+5) 10.

hollye
Télécharger la présentation

Warm Up:

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. Warm Up: h(x) is a composite function of f(x) and g(x). Find f(x) and g(x). 1. 2.

  2. THE CHAIN RULE Objective: To use the chain rule to find the derivative of composite functions.

  3. What if we wanted to take the derivative of the following: • y=(2x+5)2 • y=(2x+5)3 • y=(2x+5)10

  4. If we had y= 6x -10, dy/dx = 6. EASY BREEZY What if we wrote y as a composite function? y = 2(3x -5) Outer function: Inner function: y = 2u u = 3x-5

  5. The Chain Rule (used for composite functions) If y is a function of u, y= f(u), and u is a function of x, u=g(x), then y = f(u) = f(g(x)) and : If we have a composite function: Derivative of = derivative of X derivative of function outer function inner function (You may have composites within composites so may have to repeat)

  6. If y=f (g(x)), then y’=f ’ (g(x)) ∙ g’(x) Derivative of outer function, times derivative of inner. Take a look: y=(2x-1)2

  7. Examples: Find the derivative. 1. y = (3x +4 )3 2.

  8. Find the derivative. • y= sin(x2 + x) • y= (x3 +2x) -1 • y= cot(x2)

  9. Chain rule with products and quotients. Good times, good times…. • y = 3x(x3 +2x2)3 • y = • y = sin 2x cos2x

  10. Quotient rule…do we need it?? You decide. Find the derivative:

  11. Find the equation of the tangent line to the graph of at x = 3.

  12. Determine the point(s) at which the graph of has a horizontal tangent.

  13. Use the table of values to find the derivative. FIND at x = 2.

  14. Repeated Use of Chain Rule: Take derivative of outer function and work your way in until you have no more composites. f(g(h(x))) 1. f(x) = cos2(3x)

  15. Find the derivative. • f(x) = tan(5 – sin2t) • y =

More Related