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Product & Quotient Rules Higher Order Derivatives Lesson 2.3.

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Presentation on theme: "Product & Quotient Rules Higher Order Derivatives Lesson 2.3."— Presentation transcript:

1 Product & Quotient Rules Higher Order Derivatives Lesson 2.3

2 After this lesson, you should be able to: Find the derivative of a function using the Product Rule Find the derivative of a function using the Quotient Rule Find the derivative of a trig function Find a higher-order derivative of a function

3 Basic Rules Product Rule How would you put this rule into words?

4 The derivative of a product of 2 functions is equal to the first times the derivative of the second plus the second function times the derivative of the first.

5 Theorem 2.7 The Product Rule

6 Try Some Use additional rules to determine the derivatives of the following function

7 Try Some More Use additional rules to determine the derivatives of the following function a)

8 Try Some More Use additional rules to determine the derivatives of the following function b)

9 Try Some More Use additional rules to determine the derivatives of the following function b)

10 Try Some More Use additional rules to determine the derivatives of the following function b) NOTE!!! YOU MUST FACTOR COMPLETELY!!!!!!!!!! GET IT DOWN TO THE POINT WHERE YOU COULD SOLVE FOR THE ZEROS OF THE EQUATION!!!!!

11 Basic Rule Quotient Rule How would you put this rule into words?

12 The derivative of a quotient of 2 functions is equal to the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator all over the square of the denominator.

13 Theorem 2.8 The Quotient Rule

14 Just Checking... Find the derivatives of the given functions

15 Just Checking... Find the derivatives of the given functions

16 Just Checking... Find the derivatives of the given functions

17 Just Checking... Find the derivatives of the given functions

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27 Other Trig Derivatives Now try it out

28 Theorem 2.9 Derivatives of Trigonometric Function

29 Other Trig Derivatives

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33 JUST AN EXAMPLE OF HOW COMPLICATED THEY CAN GET!!!! CAN WE SIMPLIFY FURTHER???

34 Derivatives of the remaining trig functions can be determined the same way.

35 Find Those High Orders Find the requested derivatives

36 Find each derivative.

37 Find the derivative.

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40 Equation of a Horizontal Tangent Line Find the equations of the horizontal tangent lines for

41 Equation of a Horizontal Tangent Line Find the equations of the horizontal tangent lines for

42 Example: Write the equation of the tangent line at Equation of the Tangent Line

43 Example: Write the equation of the tangent line at Equation of the Tangent Line


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