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Pre-Calc Homework Solutions 112

# Pre-Calc Homework Solutions 112 - 112 Section 3.8 8 x 8 y 8...

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8. f ( x ) 5 y 5 } 8 x } x 5 } 8 y } Interchange x and y : y 5 } 8 x } f 2 1 ( x ) 5 } 8 x } 9. f ( x ) 5 y 5 } 3 x x 2 2 } xy 5 3 x 2 2 ( y 2 3) x 5 2 2 x 5 } y 2 2 2 3 } 5 } 3 2 2 y } Interchange x and y : y 5 } 3 2 2 x } f 2 1 ( x ) 5 } 3 2 2 x } 10. f ( x ) 5 y 5 arctan } 3 x } tan y 5 } 3 x } , 2 } p 2 } , y , } p 2 } x 5 3 tan y , 2 } p 2 } , y , } p 2 } Interchange x and y : y 5 3 tan x , 2 } p 2 } , x , } p 2 } f 2 1 ( x ) 5 3 tan x , 2 } p 2 } , x , } p 2 } Section 3.8 Exercises 1. } d d y x } 5 } d d x } cos 2 1 ( x 2 ) 5 2 } ˇ 1 w 2 w 1 ( x w 2 ) w 2 w } } d d x } ( x 2 ) 5 2 } ˇ 1 w 1 2 w x w 4 w } (2 x ) 5 2 } ˇ 1 w 2 2 w x x w 4 w } 2. } d d y x } 5 } d d x } cos 2 1 1 } 1 x } 2 5 2 } d d x } 1 } 1 x } 2 5 2 1 2 } x 1 2 } 2 5 } ) x ) ˇ x 1 2 w 2 w 1 w } 3. } d d y t } 5 } d d t } sin 2 1 ˇ 2 w t 5 } d d t } ( ˇ 2 w t ) 5 4. } d d y t } 5 } d d t } sin 2 1 (1 2 t ) 5 } d d t } (1 2 t ) 5 2 5. } d d y s } 5 } d d s } sec 2 1 (2 s 1 1) 5 } d d s } (2 s 1 1) 5 (2) 5 6. } d d y s } 5 } d d s } sec 2 1 5 s 5 } d d s } (5 s ) 5 7. } d d y x } 5 } d d x } csc 2 1 ( x 2 1 1) 5 2 } d d x } ( x 2 1 1) 5 2 5 2 Note that the condition x . 0 is required in the last step. 8. } d d y x } 5 } d d x } csc 2 1 1 } 2 x } 2 5 2 } d d x } 1 } 2 x } 2 5 2 9.
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