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2.4 The Chain Rule Objective: Find the derivative of a composite function using the Chain Rule

2.4 The Chain Rule Objective: Find the derivative of a composite function using the Chain Rule. Ms. Battaglia AB/BC Calculus. The Chain Rule. The chain rule is used to compute the derivative of the composition of two or more functions. Theorem 2.10 The Chain Rule.

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2.4 The Chain Rule Objective: Find the derivative of a composite function using the Chain Rule

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  1. 2.4 The Chain RuleObjective: Find the derivative of a composite function using the Chain Rule Ms. Battaglia AB/BC Calculus

  2. The Chain Rule The chain rule is used to compute the derivative of the composition of two or more functions.

  3. Theorem 2.10 The Chain Rule If y = f(u) is a differentiable function of u and u = g(x) is a differentiable function of x, then y = f(g(x)) is a differentiable function of x then

  4. Decomposition of a Composite Function

  5. Using the Chain Rule

  6. Differentiate

  7. Differentiating Functions Involving Radicals Find all points on the graph of for which f’(x)=0 and those for which f’(x) does not exist.

  8. Differentiating Quotients with Constant Numerators

  9. Simplify by Factoring Out the Least Powers

  10. Simplifying the Derivative of a Quotient

  11. Simplifying the Derivative of a Power

  12. Trig Functions and the Chain Rule

  13. Applying the Chain Rule to Trig Functions a. y=sin2x b. y=cos(x-1) c. y=tan3x

  14. Parenthesis & Trig Functions A. y=cos3x B. y=(cos3x)2 C. y=cos(3x)2

  15. Parenthesis & Trig Functions

  16. Repeated Application of the Chain Rule

  17. Tangent Line of a Trig Function Find the equation of the tangent line to the graph of at the point (π,1). Then determine all values of x in the interval (0,2π) at which the graph of f has a horizontal tangent.

  18. Average velocity Change in distance Change in time Ex: A billiard ball is dropped from a height of 100 ft, 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 veolcity over the time interval [1,2]. Find the instantaneous velocity at t=1.

  19. Classwork/Homework • Read 2.4, Page 137 #7-20, 45-50, 55-65 odd, 109-112

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