EXAMPLES OF DIFFERENTIAL COEFFICIENTS. 51 



< 4 



ar> + o;) 8 (&-a) 4 . 



^ = (2a& - (6a - 5 J) a - 9* z } aj (a + a:) 2 (6 - a?) 8 . 



(a + x} m (b + xy. 



1 



14. 

 15. 



16. 

 ,H. 



tan 3 x dy 4 



18. y = tanco + x. -f- = ta,nx. 



3 dx 



19. y = 



20. y = 



21. y 



= (a + a)"*- 1 (5 + a;)"- 1 { m (6 + a?) + n (a + x}}. 



1 dy _ ^ m (b + x) + n (a + a;) 



^ ' H1 "" hl 



1 - 

 a 



^ = 2x tan' 1 - + a. 

 dx a 



4. 



22. 

 23. 



24. 

 25 



20 



- , . - . 

 (a 4- 6x") log (a + 6^;") 



TT cc 

 = log tan [-+-}. 



dy 



-?- = 



-- . 

 rfa; cos a; 



e (a+>:)1 sin or. 



= e (a+a:) ' (2 (a + a?) sin a; + cos o>}. 



E2 



