Elements of the Differential And Integral Calculus With Examples And Applicati

Cover Elements of the Differential And Integral Calculus With Examples And Applicati
Elements of the Differential And Integral Calculus With Examples And Applicati
James M James Morford Taylor
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F'(x) = e (a+z)2 [2(a + a?) sins + cos a:].
24. F-kg|1og(a +&*>)]. Dy^-—-^^——.
(a -f- oa;") log (a -f- ox") 25. Y = log ^f-Han-^. *y = T^' or • -i3 +2 a;, da; 26. Y = sin ' — ■ dy = — — Vl3 Vl-Sa. '-ar 2 27. Y = e xX tan" a a;. ^ = e^T— —, + as x tan- 1 aj(l + logaj) dx [_1 + ar *-y 28. A? = c~T.
^^ = loga;; . :y= x ; . %&=, lo g* . Y 1+loga; dx* (1 -flog a;) 2 42 DIFFERENTIATION.
X 2 29. Y = 1 + 1 + 1 + etc. To infinity. X 2, xdx y = -—-; . \dy=± 1 + y ' Va 2 + i i / /a 5 X, -1% dy 1 \x + a a
...da; a; \ a; — a Q1 . Vl - x 2 + a;V2 dy V| 31 M = IO cr — ===: • — = ' Vl-a, - 2 *» (Vl-ar+a;V^)(l-^) 32. Y = log^— = rl_^ ^Vl + a, - 2 — x 33 2/ = |log^l±^+^ = log( Vl + *? + a?) ; Vl + ar — * . Dy _ 1 ' ' dx Vl+a, - 2 . (l + af)i . , . _i dy VT+x dx (l + a;)(l + ar°) CHAPTER III. INTEGRATION.
58. A function or variable is called the Integral of its differ- ential. Thus, a? is the integral of Sxrdx ; and f(x) + C, C being any constant, is the integral of f'(x)dx.


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