设函数[tex=5.571x1.286]DRqnTMbzBdK/vdZ/svToSvMJaC/5gB9wNEz3bOeiXNw=[/tex]有连续偏导数，且[tex=4.5x1.286]gsdNADfoADk0WGSc+nb2CQ==[/tex]由方程[tex=6.714x1.286]1pXL0KzCaTC+efwMufyOSyviQqtIOMpfxQxqz2ruZCmW683LIWydb2uU8lNO1uzq[/tex]所确定，求[tex=1.143x1.286]8+natyWD89VRTV/SOUMDFQ==[/tex]。

2022-07-25

设函数[tex=5.571x1.286]DRqnTMbzBdK/vdZ/svToSvMJaC/5gB9wNEz3bOeiXNw=[/tex]有连续偏导数，且[tex=4.5x1.286]gsdNADfoADk0WGSc+nb2CQ==[/tex]由方程[tex=6.714x1.286]1pXL0KzCaTC+efwMufyOSyviQqtIOMpfxQxqz2ruZCmW683LIWydb2uU8lNO1uzq[/tex]所确定，求[tex=1.143x1.286]8+natyWD89VRTV/SOUMDFQ==[/tex]。

答案：

设[tex=5.0x1.286]zrEuf0onh9/ol0VMPZRM4svwLrv3IP37elAsE0mXt+U=[/tex][tex=6.571x1.286]1pXL0KzCaTC+efwMufyOS7uRTTtY5cZvFyank7VpN8ff129ng0LaJEM4wiJ4fG2W[/tex]，则[tex=6.286x1.286]GbultviDt5JJDQ2ex16IGVwSZ4beSnTgzUtAmM4NRKBT6Suz9fGocAMltU1uFb4j[/tex]，[tex=6.929x1.357]xJ/SCPV/9gfbA4oNEgitJf7eWxlFa8AGiE5UkpeG9C3kFna5oOfkS4dXXqWQDncT[/tex]，[tex=6.857x1.286]sOAuZEK303AKnvchr/L5fjjsM9TPXXojezSrCIEcf0XzqIRR3p2rdYVR9SLWvDf7[/tex]，故[tex=10.357x2.286]V9fVXReHUrcmKJSTnoNlS6Ff1/BpV286INVZ6gU3ArPFp/pgeTLO6p+Ys/3VHXvbs4O7UnmpJb8IwoXrYQCLPmv4PFs/dPIDYZmKGciCcQUoB38FXFnDjqwvor9w8G5i0l8NQVtpjtUdPofJc+ftCQ==[/tex]，[tex=11.0x2.429]V9fVXReHUrcmKJSTnoNlS2VH85Q2O3lrqDC96Fb5StSJ6CKBiAuGLcEvWj54NzzUExF9SZeDq1sNpHAykKG2pxuo4WCu+5Ab+HvwzVSRoKZmJT1WD8L2e3YVwqQRugyWXs/m7aS9R5sN1huvIAI2Iw==[/tex]，而[tex=7.0x2.071]V9fVXReHUrcmKJSTnoNlS+UeOa20fvyFPhqUlsVsppxHE+DAAYFEIJyyaJYGFL5N8Pdvf7+MmEMei5r1sutEnNTyV019w7hRdJlYSdmfVyiY8B2HO+Yu9Gwb/4lX+yTm[/tex][tex=8.429x2.071]w126eSehsjtCDEvKiljKeW7Qmq6WwojTpivXwFIqWA9sBS8GrGcG9NLPi6ThwjNB1TiKDi2J5M88U81wWBrglIEKb9y7TMFZ/0DnVIsC6VE=[/tex]，[tex=7.0x2.214]V9fVXReHUrcmKJSTnoNlSyYi8vg6emYnFh+Uj8NYiUn2RAIFYiAFVpOT+jHRRBZYaNt4oovNqF4YhTh5+BLjr8AKQoPX5SYn0UCSz+EDgtrR0C/4Ago8HOnzy8Xmc3ka[/tex][tex=8.357x2.071]fqKVTEoC8BNACQsXprk2ePC2368HVuEneAvGFDl+84oBZ9zBSSEFHEeQu8Lypu7KbuKEpWKPGtMvnzCtA97bGw==[/tex]，所以[tex=8.429x2.214]zvgmpoh44DGjmn4STvJpg03amWTbJpY9iYrURhBgpvOR7UjwnPhG9+zyUyN64M3P1j1r6B5QMdtwCFsAtJmHoJOnu93mHnN+/urBaRXmDZKESaEk4D2GCsA0YOqEMil8[/tex][tex=11.214x2.357]j7z/IZLbAbcC45UFAMEdencTW6hx+xx+Im4qFDI85d2fR4jiYUqmY0mKGy+x3kS2VAKWrHC2Ceo3e2ZvP2rbI3oTDwn+kOM+3kO2t+j53uRe61Q7d84UVgbAGlm6jHCj[/tex][tex=10.929x2.357]u2vMtV9fnX/GuEjWskyvHIR+wgQ41loSkb6C6Z9EscvSATtQXmNY0aR5VuEXhvgxZfs17Odvg98pQU6AFP3hWrZTomtmwt279fqaIzpZyK71dD/NyseK+kSqSHxsMDmV[/tex]。

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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
求下列函数的导函数：(1) [tex=5.0x2.357]X/CieCDGJ7iPQ3YFWuscHxHrcIE/dPFa9tFyiJXze8A=[/tex](2)[tex=6.643x1.714]Oj74y/L+OxY81QME5JWMcl+7PZ2FGQswwvjgVhjq1Dmb6dBU0oAjZBW7eFBVjqo6[/tex]
2
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?
3
求函数[tex=3.286x1.429]kdT+eIE7CHPynuN6CaN40g==[/tex]（抛物线）隐函数的导数[tex=1.071x1.429]BUw1BPFU3fsJlAl/vt9M9w==[/tex]当x=2与y=4及当x=2与y=0时,[tex=0.786x1.357]Hq6bf3CacUy07X+VImUMaA==[/tex]等于什么?
4
设[tex=7.857x1.286]sWpR+4PLElO8Uw1MKkupxnNb7y3z35OdrHP/Tanh5/nVt+gIoJBCjISHPFUE279O[/tex]，其中[tex=4.5x1.286]gsdNADfoADk0WGSc+nb2CQ==[/tex]是由[tex=8.5x1.286]/ikyf7ihJGu53Kb8iS+Fnxi+6CNO6eaVqGDU0kwWgzQ=[/tex]所确定的函数，求[tex=4.786x1.286]3hV5YaUMguiZp/zXeIRVeExQRLgkmKAIT/t+NzzCuTU=[/tex]。