994 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 
Let putin Sas 
Bm "Cee 1)” 
then (v 7) “omy (L—y)” 
v= fief --..- (m times) ... y? d—y)?. 
and a =(- i seas -y (l-y)". 
Ex. 9. To find a” sin az. 
+ &. 


d 
feet = 1 daz “ aazVv—1 -arV—1 
A” sin Cer, Fry (e ° — 1)” ( e ) 
Ps 1 aWV—1 n a2V¥—1 —aV=1 n ~atV—1 
aha —1)"e ( —1)"e \ 
1 SV=1 0 SVT WT tara 
BY sae | {@ ih 
SV=1 0 -SVIL EW Ti taeWN1 
—(-1)"(e —e \"e 

1 Ader ale sete a Sa BLS 
SSS sins)" { (cos ax+ "4 VW —1 sinazx+ >) 
—(cos 2X4 1n7—V/—1 sin2X+4+1n7) (cosa +S —~/—1 sin ars) } 
i (Dn/ sin 4 cos (ax+ >) + /—1 sin (ax+ 5) 
—cos (2XFInw+ax+ 2) +/—1 sin (20a wart) } 

= 2” (/—1)"-1 sin” 5 sin (ax+ at 2A am) (sinDAF1 AZ be, 
=2" (cos nrm—V/ —1 1 sin 2 r 7) sin "5 sin (ax+~ en): 
r and A being any integers. 
Ex. 10. To find a” e™® sin ax. 


d 
A” eme sin aa (e°*—1)" (emat ae A al —eme—aaN—1) 
1 Vr1 Voi es Gaal 
=- —— {(er* -1)"e emerax Ser a =? emt—ae } 
2/1 
em x 
ae ev me 


; {(e" cosa+e"/—1 sin a—1)" (cosax+ /—1 sin az) 
