求函数的n阶导数 如何求函数的n阶导数
\u6c42\u51fd\u6570\u7684n\u9636\u5bfc\u6570
\u5982\u56fe
y ' = 2sinxcosx = sin2x
y '' = 2cos2x
y ''' = -4sin2x
y^(4) = -8cos2x
\u4e00\u822c\u5730\uff0cy^(n) = 2^(n-1) * sin[2x+(n-1)\u5140/2]
\u4f8b\u5982\uff1a
^^^y=lnx/x
y'=(1-lnx)/x^2=1/x^2-lnx/x^2
y"=-2/x^3-(1-2lnx)/x^3=-3/x^3+2lnx/x^3
\u8bb0y(n)=(-1)^(n+1)*[ an- n!dulnx]/x^(n+1)
\u6709zhiy(n+1)=(-1)^n*an (n+1)/x^(n+2)+(-1)^n* n![1- (n+1)lnx]/x^(n+2)
a(n+1)=(n+1)an+n!
a1=1\uff0ca2=3\uff0ca3=11\uff0ca4=50\uff0ca5=274
\u6269\u5c55\u8d44\u6599\uff1a
\u5bf9\u4efb\u610fn\u9636\u5bfc\u6570\u7684\u8ba1\u7b97\uff0c\u7531\u4e8e n \u4e0d\u662f\u786e\u5b9a\u503c\uff0c\u81ea\u7136\u4e0d\u53ef\u80fd\u901a\u8fc7\u9010\u9636\u6c42\u5bfc\u7684\u65b9\u6cd5\u8ba1\u7b97\u3002\u6b64\u5916\uff0c\u5bf9\u4e8e\u56fa\u5b9a\u9636\u5bfc\u6570\u7684\u8ba1\u7b97\uff0c\u5f53\u5176\u9636\u6570\u8f83\u9ad8\u65f6\u4e5f\u4e0d\u53ef\u80fd\u9010\u9636\u8ba1\u7b97\u3002
\u6240\u8c13n\u9636\u5bfc\u6570\u7684\u8ba1\u7b97\u5b9e\u9645\u5c31\u662f\u8981\u8bbe\u6cd5\u6c42\u51fa\u4ee5n\u4e3a\u53c2\u6570\u7684\u5bfc\u51fd\u6570\u8868\u8fbe\u5f0f\u3002\u6c42n\u9636\u5bfc\u6570\u7684\u53c2\u6570\u8868\u8fbe\u5f0f\u5e76\u6ca1\u6709\u4e00\u822c\u7684\u65b9\u6cd5\uff0c\u6700\u5e38\u7528\u7684\u65b9\u6cd5\u662f\uff0c\u5148\u6309\u5bfc\u6570\u8ba1\u7b97\u6cd5\u6c42\u51fa\u82e5\u5e72\u9636\u5bfc\u6570\uff0c\u518d\u8bbe\u6cd5\u627e\u51fa\u5176\u95f4\u7684\u89c4\u5f8b\u6027\uff0c\u5e76\u5bfc\u51fan\u7684\u53c2\u6570\u5173\u7cfb\u5f0f\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u9ad8\u9636\u5bfc\u6570
y'=(1/m)(1+X)^(1/m-1)y''=(1/m)(1/m-1)(1+X)^(1/m-2)………………y的n阶导数为：y (n)==(1/m)(1/m-1)...(1/m-n+1)(1+X)^(1/m-n)
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