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Pre-Calc Homework Solutions 469

Pre-Calc Homework Solutions 469 - Appendix A6 1 coth2 x 2...

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22. y 5 ln sinh x 2 } 1 2 } coth 2 x } d d y v } 5 } c s o in s h h x x } 2 1 } 1 2 } 2 (2 coth x )( 2 csch 2 x ) 5 coth x 1 (coth x )(csch 2 x ) 5 (coth x )(1 1 csch 2 x ) 5 (coth x )(coth 2 x ) 5 coth 3 x 23. y 5 ( x 2 1 1) sech (ln x ) 5 ( x 2 1 1) 1 } e ln x 1 2 e 2 ln x } 2 5 ( x 2 1 1) 1 } x 1 2 x 2 1 } 2 5 ( x 2 1 1) 1 } x 2 2 1 x 1 } 2 5 2 x } d d y x } 5 2 24. y 5 (4 x 2 2 1) csch (ln 2 x ) 5 (4 x 2 2 1) 1 } e ln 2 x 2 2 e 2 ln 2 x } 2 5 (4 x 2 2 1) 1 } 2 x 2 2 (2 x ) 2 1 } 2 5 (4 x 2 2 1) 1 } 4 x 2 4 2 x 1 } 2 5 4 x } d d y x } 5 4 25. y 5 sinh 2 1 ˇ x w 5 sinh 2 1 ( x 1/2 ) } d d y x } 5 5 } 2 ˇ x w ˇ 1 1 w 1 w x w } 5 } 2 ˇ x ( w 1 1 w 1 w x w ) w } 26. y 5 cosh 2 1 (2 ˇ x w 1 w 1 w ) 5 cosh 2 1 (2( x 1 1) 1/2 ) } d d y x } 5 5 } ˇ x w 1 w 1 w 1 ˇ 4 w x w 1 w 3 w } 5 } ˇ 4 w x 2 w 1 w 1 7 w x w 1 w 3 w } 27. y 5 (1 2 u ) tanh 2 1 u } d d u y } 5 (1 2 u ) 1 } 1 2 1 u 2 } 2 1 ( 2 1) tanh 2 1 u 5 } 1 1 1 u } 2 tanh 2 1 u 28. y 5 ( u 2 1 2 u ) tanh 2 1 ( u 1 1) } d d u y } 5 ( u 2 1 2 u ) 3 } 1 2 ( u 1 1 1) 2 } 4 1 (2 u 1 2) tanh 2 1 ( u 1 1) 5 } 2 u u 2 2 1 2 2 2 u u } 1 (2 u 1 2) tanh 2 1 ( u 1 1) 5 (2 u 1 2) tanh 2 1 ( u 1 1) 2 1 29. y 5 (1 2 t ) coth 2
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