（二阶）y=x3cos3x怎么求导？ y=cos3x的导数
y=a\uff08x\u20145\uff09^2\u5982\u4f55\u6c42\u5bfc\uff1f\u65b9\u6cd5\u4e00\uff1a\u5bf9\u6570\u6c42\u5bfc\u6cd5
y = a^x
lny = ln(a^x) = x lna
1/y * dy/dx = lna * 1
dy/dx = lna * y
dy/dx = a^x lna
\u65b9\u6cd5\u4e8c\uff1a\u5b9a\u4e49\u6c42\u5bfc\u6cd5
d/dx a^x = lim(h->0) [f(x + h) - f(x)]/h
= lim(h->0) [a^(x + h) - a^x]/h
= lim(h->0) (a^x a^h - a^x)/h
= a^x lim(h->0) (a^h - 1)/h
= a^x lim(h->0) [e^(h lna) - 1]/(h lna) * (lna)
= a^x lna lim(y->0) (e^y - 1)/y\uff0c\u4ee4y = h lna
= a^x lna * 1
= a^x lna
\u4ee4y=cosu\uff0cu=3x\uff0c\u6839\u636e\u590d\u5408\u51fd\u6570\u7684\u6c42\u5bfc\u89c4\u5219dy/dx=(dy/du)*(du/dx)
y'=(cosu)'(3x)'=-3sinu\uff0cu\u66ff\u6362\u4e3a3x\uff0c\u6700\u7ec8\u7ed3\u679cy'=-3sin3x
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y'=3x^2cos3x-3x^3sin3x
y''=6xcos3x-9x^2sin3x-9x^2sin3x-9x^3cos3x
=6xcos3x-18x^2sin3x-9x^3cos3x
Y,=3X2COS3X+X3(-3SIN3X)=3X2COS3X-3X3SIN3X
Y,,=6XCOS3X+3X2(-3SIN3X)-(9x2SIN3X+3X3*3COS3X)=6XCOS3X-18X2SIN3X-9X3*COS3X
绛旓細y'=-sin3x*(3x)'*e^(2x)+cos3x*e^(2x)*(2x)=(2cos3x-3sin3x)e^(2x)鎵浠''=(2cos3x-3sin3x)'*e^(2x)+(2cos3x-3sin3x)*[e^(2x)]'=(-2sin3x*3-3cos3x*3)*e^(2x)+(2cos3x-3sin3x)*e^(2x)*2 =(-12sin3x-5cos3x)*e^(2x)...
绛旓細y=(sin3x )^3 姹傚锛歽'=3((sin3x)^2)X(cos3x)X3=9(cos3x)(sin3x)^2
绛旓細w''=y''-27/80*sin3x-9/80*cos3x-a/2*e^(-x)鎵浠 w''+w=y''+y-3/10*sin3x-1/10*cos3x-a*e^(-x)=0 鍏剁壒寰佹柟绋嬩负r²+1=0 鐗瑰緛鏍逛紵r=卤i 鏍规嵁浜岄樁甯哥郴鏁扮嚎鎬у井鍒嗘柟绋嬬殑閫氳В鏈 w=b*sinx+c*cosx 鍏朵腑b锛宑涓哄父鏁 鎵浠 y=a/2*e^(-x)+b*sinx+c*cosx-3/80...
绛旓細绗簩绉嶆槸鍙嶅悜鐢熸垚 (Bwd) ,鎸囩敓鎴愰殢鏈哄嚱鏁,鍐嶅鍑芥暟姹傚銆傚～琛ヤ簡绗竴绉嶆柟娉曟敹闆嗕笉鍒扮殑涓浜涘嚱鏁,鍥犱负灏辩畻宸ュ叿姹備笉鍑虹Н鍒,涔熶竴瀹氬彲浠ユ眰瀵笺 绗笁绉嶆槸鐢ㄤ簡鍒嗛儴绉垎鐨勫弽鍚戠敓鎴 (Ibp) 銆傚墠闈㈢殑鍙嶅悜鐢熸垚鏈変釜闂,灏辨槸涓嶅お鍙兘瑕嗙洊鍒癴(x)=x3sin(x)鐨勭Н鍒: F(x)=-x3cos(x)+3x2sin(x)+6xcos(x)-6sin(x)...
绛旓細y'=5cos5xcos3x-3sin5xsin3x y''=5(-5sin5xcos3x-3sin3xcos5x)-3(5cos5xsin3x+3cos3xsin5x)=-25sin5xcos3x-15sin3xcos5x-15sin3xcos5x-15sin5xcos3x =-40sin5xcos3x-30sin3xcos5x 娌℃庝箞绠楋紝涓嶇煡瀵瑰惁銆
绛旓細y=x^3/cosx 鍒檡'=dy/dx=(3x^2cosx+x^3sinx)/cos^2 x 鎵浠y=(3x^2cosx+x^3sinx)/cos^2 x dx
绛旓細y=(sin3x )^3 姹傚锛歽'=3((sin3x)^2)X(cos3x)X3=9(cos3x)(sin3x)^2
绛旓細x鈭(0,蟺)3x鈭(0,3蟺)sin3x=2cos3x tan3x=2 3x=arctan2 鏌ヨ〃寰楋細3x=63.4掳鎴180掳+63.4掳鎴360+63.4掳 鎵浠ワ紝鏈3涓В 閫氳繃鏌ヨ〃鍙互姹傚緱锛歺1=21.13掳銆亁2=81.13掳銆x3=141.13掳
绛旓細cos3x=cos(蟺/2-x)===> 3x=2k蟺+(蟺/2-x)鎴 3x=2k蟺-(蟺/2-x)===> x=(4k+1)蟺/8 鎴 x=(4k-1)蟺/4銆傚洜涓篺(x)=sin3x+3cosx鐨勫懆鏈熶负2蟺锛屾墍浠ュ叾鏈澶у煎拰鏈灏忓煎彲浠ュ湪涓涓懆鏈焄0,2蟺]鍐呯爺绌躲傚湪涓涓懆鏈焄0,2蟺]鍐咃紝鍑芥暟椹荤偣鏈夊叚涓細X1=蟺/8锛孹2=5蟺/8锛X3=3...
绛旓細瑙ｏ細3x=2k蟺+胃 x=2k蟺/3+胃/3 鈭村湪涓涓懆鏈熼噷,k=1,T=2蟺/3 鎸箙A=1/2 鐢ㄦ弿鐐规硶鍛锛佸嵆3x=0锛3x=蟺/2锛3x=蟺锛 3x=3蟺/2锛3x=2蟺 瑙ｅ嚭瀵瑰簲鐨剎鍊煎氨鍙互浜(x1=0,x2=蟺/6,x3=蟺/3,x4=蟺/2,x5=2蟺/3)銆y鐨勫搴旂殑鍊间负1/2锛0锛-1/2锛0锛1/2銆
