Pre-Calc Homework Solutions 78

# Pre-Calc Homework Solutions 78 - 78 Section 3.3 dy dx d 1 4...

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10. } d d y x } 5 } d d x } 1 } 1 4 } x 2 4 2 2 } d d x } 1 } 1 3 } x 2 3 2 1 } d d x } 1 } 1 2 } x 2 2 2 2 } d d x } ( x 2 1 ) 1 } d d x } (3) 5 2 x 2 5 1 x 2 4 2 x 2 3 1 x 2 2 1 0 5 2 x 2 5 1 x 2 4 2 x 2 3 1 x 2 2 } d dx 2 y 2 } 5 } d d x } ( 2 x 2 5 ) 1 } d d x } ( x 2 4 ) 2 } d d x } ( x 2 3 ) 1 } d d x } ( x 2 2 ) 5 5 x 2 6 2 4 x 2 5 1 3 x 2 4 2 2 x 2 3 11. (a) } d d y x } 5 } d d x } [( x 1 1)( x 2 1 1)] 5 ( x 1 1) } d d x } ( x 2 1 1) 1 ( x 2 1 1) } d d x } ( x 1 1) 5 ( x 1 1)(2 x ) 1 ( x 2 1 1)(1) 5 2 x 2 1 2 x 1 x 2 1 1 5 3 x 2 1 2 x 1 1 (b) } d d y x } 5 } d d x } [( x 1 1)( x 2 1 1)] 5 } d d x } ( x 3 1 x 2 1 x 1 1) 5 3 x 2 1 2 x 1 1 12. (a) } d d y x } 5 } d d x } 1 } x 2 1 x 3 } 2 5 5 } x (2 x ) 2 x ( 2 x 2 1 3) } 5 } x 2 x 2 2 3 } (b) } d d y x } 5 } d d x } 1 } x 2 1 x 3 } 2 5 } d d x } ( x 1 3 x 2 1 ) 5 1 2 3 x 2 2 5 1 2 } x 3 2 } This is equivalent to the answer in part (a). 13. } d d y x } 5 } d d x } } 2 3 x x 1 2 5 2 } 5 5 2 } (3 x 1 2 9 2) 2 } 14. } d d y x } 5 } d d x } 1 2 5 } d d x } (1 1 5 x 2 1 2 x 2 2 ) 5 0 2 5 x 2 2 1 2 x 2 3 5 2 } x 5 2 } 1 } x 2 3 } 15. } d d y x } 5 } d d x } 1 2 5 } d d x } 1 } x 3 x 2 3 1 } 2 5 } d d x } (1 2 x 2 3 ) 5 0 1 3 x 2 4 5 } x 3 4 } 16.
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