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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7. If cs 2(1- c due (/ r - d2
7- If u = cos-l --, then will = )
l+ v dix (1+< )2
required a proof.
8. If u= /_ tan- (tan /, it is required to
/a6 b a
d u 1
prove that= -
dx a cos2 x + b sin2
9. If u = ax + b log (a cosx + b sin x), it is required to
du (a2 + b2) cos X
prove that -=
dx a cos x + b sin x
10. If u = tan x sec x +log (tan x + sec ), it is required
d u
to shew that - =2 seca3.
dx
11. Find the differential coefficients of
log (a - vx)
~u = log (a + x) log (a - x) and ue = log (a -- )
1 +2ivZ/1 — 2
12. Differentiate the functions u = log and
A/ 1-2
=tan~- (-~7%/ ~: and find the values of the diferential coefficients when x= 0 and = 1.
13. Find the successive differential coefficients of u = ee6.
14. If u = -,% it is required to prove that
d'u =- 1 -
d t == X 32(1 +log ) (1 log )3}.
15. From the following equations, sin (p = m sin q',
cos 9' 1
x = m cos qd' - cos p and y = m- - 7
*COS 20 COS 0
d2 X d y
it is required to find the values of x + d and y + -w 5 when
d4P" 0d"