9286 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 
a? 4 a Ny : 
or c— 50) d+e-ad (G2) d+6 
B= Se Mca a 
pe Ee AE py 0 AE 
S(y)t+e 


s—_— 
C4 
o(y} 
nh ae ety J (2 -)re r(v+¢ a eps} adn J (2-> pre ila +09) } 
These expressions do not appear to be susceptible of further reduction, ex- 
cept in particular cases. 
2 
Cor. Let b=F3 then 
pee er gs Ca a) + en BME oh (yO i 
To reduce this expression, it may ay be sufficiently Biles: to suppose 
the symbol 6! to include both the positive and negative signs, in which case we 
may write only one of the functions e- *° oy I ( y+ >). 


co _- east: Jee 
Now a = pe dae ( =) (See Grecory’s Hwamples, p. 499.) 
c Of 
Let ees then 
a x5 
ety Ls = ( 2022 
eee as rae ( FRA 
ey oe 2 
and z=e°" | alae 
+ eee? 
ae 4 29 
me — ts Cage 
ne ase f(9+4 aay 
SrectTIon IV. DIFFERENCES. 
22. The definition of the difference of wu, as it is commonly written by 
English authors is v.41 —2. We shall retain this definition, and generalize it by 
d d 
writing ¢* u, for vz+1, and consequently (c?*—1) «, for Ave. 
The results which we shall produce from this definition, as applied to frac- 
