86 MISCELLANEOUS EXAMPLES. 



MISCELLANEOUS EXAMPLES. 



n Tf ^a + bx dy 1 



1. Ify = tan f - , -~ = - -. 



b-ax dx 1 + x* 



a Tf -i 1 dy -i 1 x 



2. If y = x tan 1 -, -/ = tan * ---- 5 . 



x dx x l + x 



4, 



- ' dx 



_ T ,. /sin aA 8iu " dy y (x cos # sin a;) , ex 



5. If2/=(- - , -/= -- r-i ^log- . 

 V x J dx sin a; sin a; 







7. 



8. If a; = a cos ^ + 6 sin ^, and ^ = a sin ^ & cos ^, then 

 ffa: d"y <Z"a; d m y . . , f n 



> ~ 1S mde P endent of - 



9. If cos' 1 = log , then 



10. Shew that (a: 2) e x 4- x + 2 is positive for all positive 

 values of ar. 



