以变量 x和y的逐次微分来表示函数[tex=3.143x1.357]Eg6rSgUNTUffRvxyTlFbYQ==[/tex]的导数[tex=1.0x1.357]eE9dXkpN2effVrNkAbXJmGIp9WKb7xaCkkBPHXfHmGo=[/tex]及[tex=1.143x1.357]eE9dXkpN2effVrNkAbXJmBWTvFxIdNVkiZ0bLYJb+fU=[/tex]”,但不假定工为自变量.

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2022-06-14

以变量 x和y的逐次微分来表示函数[tex=3.143x1.357]Eg6rSgUNTUffRvxyTlFbYQ==[/tex]的导数[tex=1.0x1.357]eE9dXkpN2effVrNkAbXJmGIp9WKb7xaCkkBPHXfHmGo=[/tex]及[tex=1.143x1.357]eE9dXkpN2effVrNkAbXJmBWTvFxIdNVkiZ0bLYJb+fU=[/tex]”,但不假定工为自变量.

答案：

解 [tex=20.286x7.214]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[/tex][tex=25.929x4.429]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[/tex]

举一反三

内容

0
若:(1)函数 f(x)在点[tex=3.714x1.357]7VByCIzkNySq3s2l9I6f5zccNJDeV+6SQrVr3iwjgB0=[/tex]有导数,而函数g(x)在点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]没有导数;(2)函数f(x)在点[tex=3.714x1.357]7VByCIzkNySq3s2l9I6f5zccNJDeV+6SQrVr3iwjgB0=[/tex]没有导数,而函数g(x)在点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]有导数;(3)函数f(x)在点[tex=3.714x1.357]7VByCIzkNySq3s2l9I6f5zccNJDeV+6SQrVr3iwjgB0=[/tex]没有导数及函数g(x)在点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]没有导数,则函数[tex=5.643x1.357]GmtX7Vop79exGU/rpqXUYw==[/tex]在已知点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]的可微性怎样?
1
若:(1)函数 f(x)在点[tex=0.929x1.0]cjoIbYuE/p4IqfLA8eA4ZA==[/tex]有导数,而函数g(x)在此点没有导数;(2)函数f(x)和g(x)二者在点[tex=0.929x1.0]cjoIbYuE/p4IqfLA8eA4ZA==[/tex]都没有导数,可否断定它们的和[tex=7.214x1.357]oX568MWmpJJk2c1dN8FEzQ==[/tex]在点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]没有导数?
2
求下面函数的高阶导数.[tex=3.643x1.214]6v5S7oPnSz7KTMaUE7vxXQ==[/tex],求 [tex=1.0x1.357]eE9dXkpN2effVrNkAbXJmGIp9WKb7xaCkkBPHXfHmGo=[/tex].
3
求下列函数的一阶和二阶微分( $x, y, z$ 为自变量):[tex=5.071x1.643]bB9obCxDT8BFFzMaH3e7o4/N2oQhXbHxEDojTlAPvx4=[/tex]
4
设x为符号变量，[tex=16.857x1.5]K7oE2zlt+FKHLSfmZqiBUV98cWCtyhb5joSTJItity5muqZ9EiG1LkW82hkn6a+bh23UZfnWQV+au3bw1ISnhw==[/tex]，试进行如下运算：求g以[tex=2.5x1.286]fWkVFgv7dFbAsoYgN6AqJw==[/tex]为自变量的复合函数