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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.

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Warm Up:

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  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 =

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