54 EXAMPLES OF DIFFERENTIAL COEFFICIENTS. 



52. y = x". 



53. -a". 



cfo; a; 



_, 23? % _ 2 (1 - a;*) 



y- !+? a5"l + 6aj'+^ < 



a 1 



_ 



)). ?/ ^ 8111 "- .~ "7 "" / / . _ o v 



V2 dx V(! 2* - a; 2 ) 



N ^ - (sec V(l - a;)} 2 

 56. y = tanV- 



K -i 



57 ' = 



58. v = tan" 1 (w tan a?) . -~ = 3 - 2 . .. 

 rtx cos x + n sm'x 



- 



sec 



60. y = (a ; + a 



61. = t 



a \x + aj' dx x 4 a*' 



/?> . _i i, . ay ii/., \ 



62. y = sin \/(sm a:). f- \ J(l + cosec sc] 



U.X 



/> -T 2x dv 2 



oo. v = tan i . 



1- x* 



64. v = sir 



66. = 



