An elementary treatise on the differential calculus, in which the method of limits is exclusively made use of, by the Rev. M. O'Brien.

APPENDIX.
b + a cos x

203.'. cotny =

b + a cos cx
n sin w

/(a + b cos x)2 - (b + a cos?)2

dy 1
dx a + bcos
(D.)
'(1) y VE dn y = e
(1) y e, =C~.d = one?.
d n'

(2) y = ", d n =( (m-) ( +-...)(-n+)m~n.
(3) y= log d x,-1
ddv"

(4) y = sin (x + a),
(5) y = tan x,

dn y _.(9 Z w +
dx" 2

d2y
d =X

2 sin x
cos3,%

d3y 2 6sin2
dx3 cos2 + cos4
4 6
Cos'2a COS4
&c. &c.

Hence assume that in general
d2n-ly A, Bn C,. _. -+-+.*..+
dwaen-~ cos 2v cos4 Cosa x
and we find
d2"y 2 A4 sin x 4 B, sinx 6 C, sin x
dx2n - cos3x cos5x cos7x