n阶导数怎么求
y = 2sinxcosx = sin2xy = 2cos2x
y = -4sin2x
y^(4) = -8cos2x
一般地，y^(n) = 2^(n-1) * sin[2x+(n-1)兀zhi/2]
扩展资料
基本初等函数导数公式主要有以下：
y=f(x)=c (c为常数),则f'(x)=0
f(x)=x^n (n不等于0) f'(x)=nx^(n-1) (x^n表示x的n次方)
f(x)=sinx f'(x)=cosx
f(x)=cosx f'(x)=-sinx
f(x)=a^x f'(x)=a^xlna(a>0且a不等于1,x>0)
f(x)=e^x f'(x)=e^x
f(x)=logaX f'(x)=1/xlna (a>0且a不等于1,x>0)
f(x)=lnx f'(x)=1/x (x>0)
f(x)=tanx f'(x)=1/cos^2 x
f(x)=cotx f'(x)=- 1/sin^2 x
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绛旓細y = 2sinxcosx = sin2x y = 2cos2x y = -4sin2x y^(4) = -8cos2x 涓鑸湴锛寉^(n) = 2^(n-1) * sin[2x+(n-1)鍏zhi/2] 鎵╁睍璧勬枡 鍩烘湰鍒濈瓑鍑芥暟瀵兼暟鍏紡涓昏鏈変互涓嬶細y=f(x)=c (c涓哄父鏁),鍒檉'(x)=0 f(x)=x^n (n涓嶇瓑浜0) f'(x)=nx^(n-1) ...
绛旓細瑙ｆ瀽濡備笅锛氳瀵焬=x锛坸-1锛夛紙x-2锛夛紙x-3锛夆︹︼紙x-n锛夌殑鏈楂樻鏁伴」涓簒^锛坣+1锛夛紝姹俷闃跺鍚庢垚涓猴紙n+1锛夛紒x 绗簩楂樻鏁伴」涓-锛1+2+3+鈥︹+n锛墄^n锛屾眰n闃跺鍚庡彇绯绘暟鎴愪负-n锛坣+1锛/2 鎵浠鐨n闃跺鏁涓猴紙n+1锛夛紒x-n锛坣+1锛/2 瀵煎嚱鏁 濡傛灉鍑芥暟y=f锛坸锛夊湪寮鍖洪棿鍐呮瘡涓...
绛旓細浜岄樁瀵兼暟鏄鏁扮殑瀵兼暟,灏嗗鏁板啀姹備竴娆″.涓夐樁灏辨槸瀵兼暟鐨勫鏁扮殑瀵兼暟,姹傚涓夋.n闃跺鏁灏辨槸姹俷娆″.绠鍗曠殑瑙勫緥鏈夛細x^n鐨刴闃跺鏁版槸n(n-1)鈥︹(n-m+1)x^(n-m)e^x鐨刵闃跺鏁颁粛鏄痚^x sin x鐨刵闃跺鏁版槸sin(x-n蟺/2蟺)cos x鐨刵闃跺鏁版槸cos(x-n蟺/2蟺)
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绛旓細f4(x)=3sinx - 3^2sinx + 3^3sinx - 3^4sinx +3^4sin^3x 閫氶」瑕佸垎4n+1锛4n+2锛4n+3锛4n+4鏉ヨ璁 4n+1闃娆瀵兼暟鍏辨湁4n+2椤 f4n+1(x) = 3cosx -3^2cosx + 3^3cosx - 3^4cosx + ... + 3^(4n+1)cosx -3^(4n+1)cos^3x 4n+2闃舵瀵兼暟鍏辨湁4n+3椤 f4n+2(x)...
绛旓細姹俷闃跺鏁娌℃湁缁熶竴鐨勫叕寮忥紝閮介渶瑕佺粨鍚堥鐩潵鍏蜂綋鍒嗘瀽鐨 锛1锛墆=e^(ax+b)y'=a*e^(ax+b)y''=a^2*e^(ax+b)...y^(n)=a^n*e^(ax+b)锛2锛墆=(1-x)/(1+x)=(2-1-x)/(1+x)=2/(1+x)-1=2*[(1+x)^(-1)]-1 y'=2*(-1)*(1+x)^(-2)y''=2*(-1)*(-2...
绛旓細鏈変竴涓寮︾殑n闃跺鏁鍏紡濡備笅锛歴inx鐨刵闃跺锛漵in锛坸锛媙鍏锛2锛夛紝鎵浠绛変簬闆舵椂锛宯闃跺鍊间负锛歴in锛坣鍏锛2锛夛紳0 锛宯锛2m锛岋紳 锛堜竴1锛夛季锛坢涓1锛 n锛2m涓1銆傛墍浠ワ細sinx锛漻涓x锛3锛3锛岋紙涓1锛夛季锛坣涓1锛墄锛撅紙2n涓1锛夛紡锛2n涓1锛夛紜o锛坸锛撅紙2n涓1锛夛級銆
绛旓細y'=1/(1+x)=(1+x)^(-1)y''=-1*(1+x)^(-2)y'''=-1*(-2)*(1+x)^(-3)=2*(1+x)^(-3)y'''=2*(-3)*(1+x)^(-4)=-6*(1+x)^(-4)鎵浠^(n)=(-1)^(n+1)*(n-1)!*(1+x)^(-n)
