262 



PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 



then y^ =2 . f ^^ 



-ir~, + 



J • % 



3 . 4 . 5 ot2 .^1 3 . 4 . 5 . 8 . 9 . 10 m'^x'- 



77 — &C. 



d x^ m^ x" 3 . 4 . 5 W x^ 



m^xi dx^ 



+ &c. 



d'y 



d 



X' \2x m'x<') dx^ 4x- dx ^ %x^^-'~ 



3^. B^+ ?^ +^ +&c. = B(,t- ^-^ 



+ T 



2 -3.7.8 



=B-^ suppose 



then ^3 = 



2.3 f . # . i ?«^ »2 "*" J . 5 . J . H 



2.3 



■^ i • I • I- ■ ¥ • y • y »«* «' 



— &c. 



d^ \/ocy^ = } ■ j ■ f .y^ , J: 2.3 



dx^ 





2.3 m^ xi I . I . J »j4 «y 



mr x^ ax~ 



T^ + &C. 



35 i 1 rf2« 



16 



/_3 1_ \ rf^3 ?_ ^ _§_ 



\2x m^xy dx^ 4x' dx '^8x'^^~ 



35 

 16 



4°. 



B. ^ B3 B 



a + 1 a + as + '"C- — y== I -; -— j-, + &C. ] 



' x^ a- = mV ~l\x^ 4 . 5 . 6 W!^ x^ J 





then 



»/„=-2^J- 



4 . 5 . 6 »8^ 3"» 



+ &c. 



d^ ^xy. 1 . 1 , 



'~d'x'^ = ^^' ~ "^^^ "= ^?Tv-^* t'l^ ^^™^ equation as for y^,. 



C+y: +^J+&c. = C(l- 



=c 



dx* 

 1 



1.2 J . 1 . S »«2 ^3 



3.4 



+ &c. 



rf^ -Jccy , _ 5 3 j_ 1 



rfir' 2 ■ 2 '2 V.r »»-«■'-■ *''• 



d'y^ /3 1_ \ d-y^ _ _3_ rf^ _3_ _ 15 



rfir' "*" V2ir m'^xo) dx^ 4^^ rfa' "*" 8i^^= ~ 8^ 



