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chapter 3 - Chapter 3 Exercises 3.1 1 d x 1 x 3 5 x 2 dx =...

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131 Chapter 3 Exercises 3.1 1. d dx [( x + 1)( x 3 + 5 x + 2)] = ( x + 1)(3 x 2 + 5) + ( x 3 + 5 x + 2) = 4 x 3 + 3 x 2 + 10 x + 7 2. 3 5 ( 3 11)( 1) d x x x dx + + 3 4 2 4 3 2 ( 3 11)(5)( 1) (3 3)( 1) ( 1) (8 3 18 52) x x x x x x x x x = + + + + = + + 5 3. 4 5 4 4 3 8 5 4 3 (2 1)( 1) (2 1)( 5 ) (8 1)( 1) 18 6 5 8 1 d x x x dx x x x x x x x x x + + = + + + = − + + 5 4. 2 2 2 ( 3)(2 1) ( 3)(2) (2 )(2 1) 6 2 6 d x x dx x x x x + = + + = + x 5. 2 4 ( 1) d x x dx + 2 3 2 2 2 3 2 4 2 3 2 (4)( 1) (2 ) (1)( 1) 8 ( 1) ( 1) ( 1) (9 1) x x x x x x x x x = + + + = + + + = + + 4 6. 2 2 (7 1) d x x dx 2 2 (2)(7 1)(7) (2 )(7 1) 2 (7 1)(14 1) x x x x x x x = + = 7. d dx [( x 2 + 3)( x 2 3) 10 ] = ( x 2 + 3)(10)( x 2 3) 9 (2 x ) + ( x 2 3) 10 (2 x ) = 2 x ( x 2 3) 9 (11 x 2 + 27) 8. 4 [( 1)(7 2)] d x x dx + [ ] 3 4[( 1)(7 2)] ( 1)(7) (1)(7 2) x x x x = + + + [ ] 3 (56 20) ( 1)(7 2) x x x = +
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