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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