Chapter11.4 - Chapter 11.4 Page 613 Theorem 1: [ ] ( 29 [ ]...

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Unformatted text preview: Chapter 11.4 Page 613 Theorem 1: [ ] ( 29 [ ] ) ( ' ) ( ) ( 1 ' x f x f n x f n n =- Example 3. Find the derivatives for the following functions: (A) 4 ) 1 3 ( ) ( + = x x f 3 3 1 4 4 ) 1 3 ( 12 ) 3 ( ) 1 3 ( 4 )' 1 3 ( ) 1 3 ( 4 ]' ) 1 3 [( ) ( ' + = + = + + = + =- x x x x x x f (B) 7 3 ) 4 ( + = x y 6 3 2 2 6 3 ' 3 1 7 3 7 3 ) 4 ( 21 ) 3 ( ) 4 ( 7 ) 4 ( ) 4 ( 7 ]' ) 4 [( ' + = + = + + = + =- x x x x x x x y (C) ( 29 ( 29 ( 29 ( 29 [ ] ( 29 ( 29 ( 29 ( 29 ( 29 4 2 4 2 2 1 3 2 ' 3 2 3 2 3 2 4 3 6 1 2 4 3 ' 4 4 3 4 4 4 1 + +-- = + + + - = + + + + - = + + = + + = + +----- t t t t t t t t t t t t t t dt d t t dt d Example. Find an equation of the tangent line at x = 2 for 12 2 ) ( 2 + = x x x f . The derivative , rule product x x x x x f _ )' 12 2 ( 12 2 )' ( ) ( ' 2 2 + + + = Rule Chain x x x x x x x x x _ ] )' 12 2 ( ) 12 2 ( 2 1 [ ) 12 2 ( 2 ]' ) 12 2 [( ) 12 2 ( 2 1 2 1 2 2 1 2 1 2 2 1 + + + + = + + +...
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This note was uploaded on 04/09/2008 for the course MAT 220 taught by Professor For during the Spring '08 term at Community College of Allegheny County.

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Chapter11.4 - Chapter 11.4 Page 613 Theorem 1: [ ] ( 29 [ ]...

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