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

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4du u (a- 9,u)
47. If uw (a - x) = a3, then d- -
d- B (a- x)
du X (2u+Sx)
48. If u3 - ux - 3= then =
d x 32u --
49. If (2 + 2)3- 4a2u22 =0, then
du S 3u4 + (6xc2-4a2) u2 + 3x
d o \3 u + 3+(6a2 -4a2) 2 + 341 *
50. If u2 + x = 2 a V' u, then
du x {a- 'V Zu,
dta? ^u a + A/M2 u2
51. If: = (a + u)b v2 - 2, then
du u (a + u) (b2 _ u2)
drv x (ab2 — u3)
52. If u =-. + x2 + I3 + a4 + &c. to n terms, then
du x"Z- 1
-- =1 + + xS + X + &c. to n terms --
dx x-.1
53. If u = v/2 + + + a2 + v&. ininf.: then
du 2
d? / — /4x + 4a + '
54. If u =V 2+ 2 ax + \V2 2+2 ar + &c. innf.:
due 2 (iv + a)
d. - V/42 + 8aiv+ 1