25G 



PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 



A 



log a; 1 



; \/ — 1 a:" d jn + i 



dn i^ 



n 





1 — mv—l 



Is + i 



Ex.3. 



Suppose 



or 



y — aV—l a:— 4 =0- 

 y^Ja^x-"; then 





1 /'■ + * n \ 



Hence the lowest value of r is 0, and the values succeed at intervals of k 

 y 



A A 

 A+ 7^ + — + &c., with the relation expressed by (1). By substitution 



A, = -iSA,A,=-l/lA„A3 = -li&e. 

 ' a\ - a/I ' ' a,2 



A, = -V^A;A, = i-/IiiA-l 

 ^ a '^ 



A=^A 

 a- 



«'/¥/l 



A __l/iMA--^A A -ifflii2 = lZ-A 

 '~ a^/l/l/2 «' '^~«VI/|/2/| a^l.s"^ 



«' /I /3 

 &c., &c., so that 



_ f _2_ 2- 2-' 



A..-^.^A=-^^A,A„=^^AM=l.-e-.A 



a= 1.2 



" as 1 . 3 ,3/7 0=1.3.5 



&c. 



-^'^fe ^ r^ ^ r/^^ -^ ^') } 



Let 



then 



22 



■T— O + &C. 





rfa- 



2 V^' a2 «■? 



or 



i^i 



2 V^ a^ a?' ■ 



