导数

导数 -...

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Unformatted text preview: • Xý • ª6 •( ý À 1.y =f (x) 1 2.y =f (x) 1 ·•iè • k èª 3. è•* i· ª 1 • + t f ′( x) = lim ∆x →0 ∆y f ( x + ∆x) − f ( x) = lim ∆x ∆x→0 ∆x x0 ù· .¥ X Á˜ IH f ′( x0 ) = lim ∆x →0 ∆y Hx •* ª · ∆ y=f(x) 1 P 1 x0,f(x0)) x0 1 f ( x0 + ∆x) − f ( x0 ) f(x) 1 ∆x S=S 1 • ti è·* ª s (t + ∆t ) − s (t ) V = lim ∆t ∆t →0 • ti è·* ª • i è·* ª S1 t1 4M. hÚ³ª6 1 11 △y y=f 1 x 1 1 2H = ∆y ∆x x0 ˆõ 31 lim ∆y ∆t →0 ∆x 5. h³ª ÚM 6ª ³ h ÚM y=f(x) 1 f6ª ³ Ú M h ′(x) f 1 (x) 1 y 1 a=s 1 (t) 1 △ s=s(5+△t)-s(5)=(5+△t)2-52=△t2+10△t 1 ∆s = ∆t + 10 ∆t ∆s v = lim = lim (∆t + 10) = 10 ∆t →0 ∆t ∆t →0 (2) 1 f 1 • x h·ª6 d B· A. f ′( x 0 ) 1 31 B. 2 f ′( x 0 ) x=x0 8 ª· • d lim h →0 f ( x 0 + h) − f ( x 0 − h) h D.0 C. -2 f ′( x 0 ) f1 x1 lim ∆x → 0 f ( x0 + 3∆x) − f ( x0 ) = 1, ∆x f ′( x0 ) A. 1 1 4< < A. 1 0 B. 0 C. 3 D. f ( x0 + ∆x) − f ( x0 ) ′( x0 ) = lim f△ ∆x ∆x →0 B. 1 0 C. 1 0 D. 1 1 3 •x 8 d D à C 0 01 1£. H9 ´ª6 • • • • c′=0(c 1 (xm) ′=mxm-1(m∈Q) (sinx) ′=cosx (cosx) ′=-sinx • (ex) ′=ex • (ax) ′=ax lna • (lnx) ′= 1 x 1 (log a x)′ = log a e x 2. ˆ…ù 1 u±v) ′=u′±v′ (uv) ′=u′v+uv′ u u ′v − uv ′ ( )′ = (v ≠ 0) 2 v v 6 · 3. ø ª •k yx′=yu′·ux′ 2 ÐHù 1 1 1 y= 1 2 1 y= f (1)y′= x − 2 (3 x + 1) 2 e cos x 1 2x 1 3 1 y=ln(x+sinx) log 1 4 1 y= 3 ( x − 1) 2 − 1 ( x − 2) 2 ⋅ (3 x + 1) 2 + x − 2 ⋅ 2 ⋅ (3 x + 1) ⋅ 3 2 (3 x + 1) 2 = + 6(3 x + 1) ⋅ x − 2 2 x−2 (2) (3) 1 1 + cos x y′ = ⋅ ( x + sin x)′ = x + sin x x + sin x ′ = 2e 2 x ⋅ cos x − e 2 x ⋅ sin x y (4) 2 x log 3 e 1 2 y′ = 2 log 3 e ⋅ ( x − 1)′ = x −1 x2 −1 31 01 − 3 2 3 π ′′( ) = f 2 1 6 4 2 1 ∵ y′=2ax+b, ∴ ∵ ∈ ¨ ¨1¨ 1 ¨ 1 ¨ ¨¨ ¨ ª• · y ′ | x = 2 = 4a + b = 1····· ① ∴ a+b+c=1····② 4a+2b+c= -1···③ a=3,b=-11,c=9 ①②③ 2 1 -1a 6· ª h• 2. 1 bc À t• ∴ 2 1 0 H•·ª b y=6· • b H ª 1 x y ′ x=a 1 =− 2 a P1 a1 b1 6· • Η ªb ∵ ∈ 2 1 0 ¨óí· ∵ P 1 a,b ˜ ˜˜˜ ①② H•* b ª · 1 y − b = − 2 ( x − a) a y∴ = 1 x a2b=2-a ------① ab=1 ------------② a=1,b=1 x+y-2=0 4 1 11 1 21 • h h· ª 1 31 l1 1 y=x4 è· •gª π1 ( k, ) y=cosx ¸ DP @( 2 3 1 23 π y− = (x − ) .3 2 3 π ( ,0) 2 • 4 è·* gª 4x-y-3=0 . y=sinx 1 0 1· • 0 h 6ª h l1 1 l2 hh* • ª · l2 1 90° . .0 6+△t. 1 6. y=cosx 1 14 1 s=t2+3, h·* •hª 3,3+Δt 2 . 1 t=3h h·* •ª 1 ` • ª · 1.À • + t 1 @. @E kn @ 7 ( t +À•c f(x) 1 x8 0 . (a,b)t +À c • f′(x0), t +À•c f′(x), 1 f′(x0)=f′(x)|x=x (a,b) 1 2.`* • ª · ( bt E j 3 . ÁN ·* PH ˜• Ž + tª ( bt E j 01 01 → ˜ ˜ ˜ → → • e Ø·ª lim f ( x) = x → x0 f ( x0 ) ? y øj•·ª* 1 O1 1 3 p o y=x x 8Ž O· ª (1. @ Et k j+ •À + t 2. 1 1· 3. t (+ E@ jk Ž M èª * (t E+ j@ E ( k 1. △ y 1 △8 x 8 88 =.tá* † =u t HªN+ • cÁ0 H= . ˜t Ž=· + ·* Oª . 8 8 △8 x 8 88 △ x →0 1 . 1.O ·* ¨Ž ª 2. . ¨ªŽ O * · p141. .B 5ªŽ O * ¨ · 6 . 2002.4 ...
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This note was uploaded on 09/28/2010 for the course MATH 210 taught by Professor Drzhao during the Spring '10 term at Kansas State University.

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