DIFFERENTIAL COEFFICIENTS. 49 



. x dy 1 x 



y = sm - . -f- = - cos - . 



a dx a a 



x dy 1 . x 



y = cos - . -f = sm - . 



a dx a a 



x dy 1 ,# 



2/ = tan-. -/=-sec-. 



a aa; a a 



.a? c?v 1 a? 



v = cot - . ~ = cosec - . 



a ax a a 



. x 



j , sin - 



x dy 1 a 



y = sec - . ~ = - . 



a dx a *x 



cos - 



a 



x 



x dv I 



y cosec 



x dy _ 1 a 



dx a . 



sm 

 a 



y Sm a' dx 



~x dy 



= cos . -#- = 



ft dx 



>i a; dy a 



v/ = tan 1 - 



ct * cfo a 8 + a;* * 



, -i a? <&/ a 



V = COt l - . -f- = 5 ; . 



a rfic a^ + a? 



-i& dy _ a 



& dx xtj(x z a 2 



dy _ 



a dx x*J(3? G?) ' 



_, x dy 1 



?/ = vpr^ ^ _ ______^___ 



a* ^"^aa;-* 1 )' 



T. D. C. E 



