Copy_of_3.3notestouse

Copy_of_3.3notestouse - The Product Rule uv ( ) = The...

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Calculus Section 3.3 Page15 3.3 Rules for Differentiation Basic Rules Derivative of a Constant c ( ) = Power Rule x n ( ) = Constant Multiple Rule c u ( ) = Sum and Difference Rule u ± v ( ) = Example 1 Differentiating using the basic rules Find dy dx if a) y = x 3 + 6 x 2 - 5 3 x + 16 b) y = x 4 4 + x 2 8 + 5 x c) y = 5 x 2 + 1 x - 3
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Calculus Section 3.3 Page 16 d) y = x + 3 x - 1 e) y = x 2 + 3 2 x Example 2 Finding Tangent Lines Use the results from part e) to find the equation of the tangent to the curve y = x 2 + 3 2 x at the point 1,2 ( ) . Support your answer graphically. Example 2 Finding Horizontal Tangents a) Does the curve y = x 4 - 2 x 2 + 2 have any horizontal tangents? If so, where?
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Calculus Section 3.3 Page17 b) Determine the x -values where the curve y = 0.2 x 4 - 0.7 x 3 - 2 x 2 + 5 x + 4 has horizontal tangents. More Differentiation Rules
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Unformatted text preview: The Product Rule uv ( ) = The Quotient Rule u v = Example 3 Differentiating a Product Find f x ( ) if f x ( ) = x 2 + 1 ( ) x 3 + 3 ( ) Example 5 Working With Numerical Values Let y = uv be the product of the functions u and v. Find y 2 ( ) if u 2 ( ) = 3, u 2 ( )= -4, v 2 ( )= 1, and v 2 ( ) = 2 Example 6 Differentiating a Quotient Differentiate f x ( ) = x 2-1 x 2 + 1 Calculus Section 3.3 Page 18 Example 7 Second and Higher Order Derivatives Find the first four derivatives of y = x 3-5 x 2 + 2 Assignment II3 Page 120 121 #1 12 all, 13, 14, 16, 17, 18, 23 31 odd, 34...
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This note was uploaded on 02/04/2011 for the course MATH 116 taught by Professor John during the Spring '10 term at St. Michael.

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Copy_of_3.3notestouse - The Product Rule uv ( ) = The...

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