微积分公式 微积分基本公式？
\u5fae\u79ef\u5206\u57fa\u672c\u516c\u5f0f\u6709\u54ea\u4e9b\uff1f(1)\u5fae\u79ef\u5206\u7684\u57fa\u672c\u516c\u5f0f\u5171\u6709\u56db\u5927\u516c\u5f0f\uff1a
1.\u725b\u987f-\u83b1\u5e03\u5c3c\u8328\u516c\u5f0f,\u53c8\u79f0\u4e3a\u5fae\u79ef\u5206\u57fa\u672c\u516c\u5f0f
2.\u683c\u6797\u516c\u5f0f,\u628a\u5c01\u95ed\u7684\u66f2\u7ebf\u79ef\u5206\u5316\u4e3a\u533a\u57df\u5185\u7684\u4e8c\u91cd\u79ef\u5206,\u5b83\u662f\u5e73\u9762\u5411\u91cf\u573a\u6563\u5ea6\u7684\u4e8c\u91cd\u79ef\u5206
3.\u9ad8\u65af\u516c\u5f0f,\u628a\u66f2\u9762\u79ef\u5206\u5316\u4e3a\u533a\u57df\u5185\u7684\u4e09\u91cd\u79ef\u5206,\u5b83\u662f\u5e73\u9762\u5411\u91cf\u573a\u6563\u5ea6\u7684\u4e09\u91cd\u79ef\u5206
4.\u65af\u6258\u514b\u65af\u516c\u5f0f,\u4e0e\u65cb\u5ea6\u6709\u5173
(2)\u5fae\u79ef\u5206\u5e38\u7528\u516c\u5f0f\uff1a
Dx sin x=cos x
cos x = -sin x
tan x = sec2 x
cot x = -csc2 x
sec x = sec x tan x
csc x = -csc x cot x
sin x dx = -cos x + C
cos x dx = sin x + C
tan x dx = ln |sec x | + C
cot x dx = ln |sin x | + C
sec x dx = ln |sec x + tan x | + C
csc x dx = ln |csc x - cot x | + C
sin-1(-x) = -sin-1 x
cos-1(-x) = - cos-1 x
tan-1(-x) = -tan-1 x
cot-1(-x) = - cot-1 x
sec-1(-x) = - sec-1 x
csc-1(-x) = - csc-1 x
Dx sin-1 ()=
cos-1 ()=
tan-1 ()=
cot-1 ()=
sec-1 ()=
csc-1 (x/a)=
sin-1 x dx = x sin-1 x++C
cos-1 x dx = x cos-1 x-+C
tan-1 x dx = x tan-1 x- ln (1+x2)+C
cot-1 x dx = x cot-1 x+ ln (1+x2)+C
sec-1 x dx = x sec-1 x- ln |x+|+C
csc-1 x dx = x csc-1 x+ ln |x+|+C
sinh-1 ()= ln (x+) xR
cosh-1 ()=ln (x+) x\u22651
tanh-1 ()=ln () |x| 1
sech-1()=ln(+)0\u2264x\u22641
csch-1 ()=ln(+) |x| >0
Dx sinh x = cosh x
cosh x = sinh x
tanh x = sech2 x
coth x = -csch2 x
sech x = -sech x
绛旓細- 涓夎鍑芥暟鐨绉垎鍏紡锛屽sin x, cos x, tan x绛夌殑绉垎鍏紡銆- 瀵规暟鍑芥暟銆佹寚鏁板嚱鏁般佸箓鍑芥暟鐨勭Н鍒嗗叕寮忋- 鍙嶄笁瑙掑嚱鏁扮殑绉垎鍏紡锛屽sin^(-1)(x), cos^(-1)(x)绛夌殑绉垎鍏紡銆- 鍙屾洸鍑芥暟鐨勭Н鍒嗗叕寮忥紝濡俿inh x, cosh x, tanh x绛夌殑绉垎鍏紡銆備互涓婅繖浜涘叕寮忔槸寰Н鍒涓渶鍩虹涔熸槸鏈閲嶈鐨...
绛旓細寰Н鍒鐨勫熀鏈鍏紡鍖呮嫭寰垎鍜岀Н鍒嗕袱涓柟闈備互涓嬫槸鐩稿叧鍏紡鐨勬敼鍐欏拰娑﹁壊锛屽悓鏃剁籂姝ｄ簡鍙兘鐨勯敊璇紝骞剁‘淇濅簡璇箟鐨勫噯纭с傚井鍒嗗叕寮忥細1. 鍩烘湰鍑芥暟寰垎鍏紡 - \( \frac{d}{dx}(x^n) = nx^{n-1} \)- \( \frac{d}{dx}(\sin x) = \cos x \)- \( \frac{d}{dx}(\cos x) = -\sin...
绛旓細1. 鐗涢】-鑾卞竷灏艰尐鍏紡锛氳繖涓鍏紡鏄寰Н鍒瀛︾殑鍩虹煶涔嬩竴锛屽畠纭珛浜嗕笉瀹氱Н鍒嗕笌寰垎涔嬮棿鐨勮仈绯汇傚叿浣撳湴锛屽叕寮忚〃杈句负鈭(from a to b) f(x) dx = F(b) - F(a)锛屽叾涓璅(x)浠ｈ〃f(x)鐨勪竴涓師鍑芥暟銆傝鍏紡鐨勯噸瑕佹у湪浜庡畠寤虹珛浜嗗畾绉垎涓庝笉瀹氱Н鍒嗕箣闂寸殑妗ユ锛屼娇寰楀畾绉垎鐨勮绠楀彲浠ラ氳繃瀵绘壘鍘熷嚱鏁版潵...
绛旓細鍩烘湰鐨寰Н鍒嗗叕寮鏈16涓紝濡備笅鎵绀猴細
绛旓細寰Н鍒鐨勫熀鏈繍绠鍏紡锛1銆佲埆x^伪dx=x^(伪锛1)/(伪锛1)+C (伪鈮狅紞1)2銆佲埆1/x dx=ln|x|+C 3銆佲埆a^x dx=a^x/lna+C 4銆佲埆e^x dx=e^x+C 5銆佲埆cosx dx=sinx+C 6銆佲埆sinx dx=-cosx+C 7銆佲埆锛坰ecx)^2 dx=tanx+C 8銆佲埆锛坈scx)^2 dx=-cotx+C 9銆佲埆secxtanx dx=...
绛旓細寰Н鍒鐨勫熀鏈叕寮忓寘鎷細瀵兼暟鍏紡锛氬鏋滃嚱鏁皔=f(x)鍦ㄧ偣x澶勬湁瀵兼暟锛岄偅涔堣鍑芥暟鍦▁澶勭殑瀵兼暟鍙互鐢ㄤ互涓嬪叕寮忚〃绀猴細(f(x))' = f'(x)銆傚父瑙佺殑瀵兼暟鍏紡鏈夛細(C)' = 0, (x^n)' = nx^(n-1), (sinx)' = cosx, (cosx)' = -sinx, (e^x)' = e^x, (lnx)' = 1/x绛夈绉垎鍏紡锛...
绛旓細寰Н鍒鍩烘湰鍏紡16涓細
绛旓細寰Н鍒嗗叕寮鏄細Dx sin x=cos x锛宑os x = -sin x锛宼an x = sec2 x锛宑ot x = -csc2 x锛宻ec x = sec x tan x绛夌瓑锛岀Н鍒嗘槸寰垎鐨勯嗚繍绠楋紝鍗崇煡閬撲簡鍑芥暟鐨勫鍑芥暟锛屽弽姹傚師鍑芥暟锛屽湪搴旂敤涓婅繕琚ぇ閲忓簲鐢ㄤ簬姹傚拰锛屽嵆姹傛洸杈逛笁瑙掑舰鐨勯潰绉紝杩欏阀濡欑殑姹傝В鏂规硶鏄Н鍒嗙壒娈婄殑鎬ц川鍐冲畾鐨勩傚彟澶栦富瑕佸垎涓...
绛旓細琛ュ厖鍥炵瓟锛 寰Н鍒璁＄畻娉曞垯鏈夊緢澶: 鈥濆叾瀹炲井鍒嗙殑瀹炶川灏辨槸姹傚鈥1.鍩烘湰鍑芥暟寰垎鍏紡 dx^n=nx^(n-1)dx dsinx=cosxdx dcosx=-sinxdx dtanx=(secx)^2dx dcotx=-(cscx)^2dx dloga x=1/xlnadx da^x=a^xlnadx de^x=e^xdx dlnx=1/xdx 2.寰垎鏈韩鐨勮繍绠楀叕寮(浠ヤ笅f,g鍧囦负鍏充簬x鐨勫嚱鏁)d...
绛旓細鎬荤殑鏉ヨ锛寰Н鍒鍩烘湰鍏紡鏄井绉垎瀛︿範鐨勫熀纭鍜屾牳蹇冿紝鎺屾彙杩欎簺鍏紡涓嶄粎鍙互甯姪鎴戜滑瑙ｅ喅鍚勭绉垎闂锛屾洿鍙互鍩瑰吇鎴戜滑鐨勬暟瀛︽濈淮鍜岃В鍐抽棶棰樼殑鑳藉姏銆傚洜姝わ紝鍦ㄥ涔犲井绉垎鐨勮繃绋嬩腑锛屾垜浠簲璇ユ繁鍏ョ悊瑙ｅ拰鎺屾彙杩欎簺鍏紡锛屽悓鏃朵篃瑕佹敞鎰忔帰绱㈠畠浠箣闂寸殑鑱旂郴鍜岃浆鍖栧叧绯伙紝浠ヤ究鏇村ソ鍦板簲鐢ㄥ畠浠В鍐冲疄闄呴棶棰樸
