设方程 [tex=4.714x1.357]JKZ+ROFvw8Qo/AVLdzU9lg==[/tex]确定隐函数[tex=4.286x1.357]W53kgHVhR4iPLH8xcb4zFA==[/tex] 求 [tex=1.286x1.0]17Sp5sHpSxcK9tRqPycyLA==[/tex]

2022-07-26

设方程 [tex=4.714x1.357]JKZ+ROFvw8Qo/AVLdzU9lg==[/tex]确定隐函数[tex=4.286x1.357]W53kgHVhR4iPLH8xcb4zFA==[/tex] 求 [tex=1.286x1.0]17Sp5sHpSxcK9tRqPycyLA==[/tex]

答案：

解 根据链式规则，并采用注释 [tex=1.0x1.0]5ll/4oTq8VGGY6gN6eTenQ==[/tex]中的记号，则关于 [tex=0.571x0.786]ZKO2xs0EgSemzoH7MSmYTA==[/tex] 的偏导数为[tex=8.214x1.429]rF35fRkZJ9nrOYMQFJLmQsrvON4Fdh9YNaECsQfJXIDrRs7h6dt6RkTJjU3aq3Fv4wuiSeU7MH18HTc7NGJ/eGCGQ8dqAfW/RtHhO2PtrG4=[/tex] （*）解出[tex=4.214x2.786]uz3QNwNlW+AJ3yBrNyXaHajfroBATOtBDX2ELnvdRYDyZ8l4jfwleLkjQNd3ZsxJ+pJE3qJ6ogooVyKaAsQZfQ==[/tex] [认为 [tex=3.571x1.429]X32XpXvxdV+hmQmPRBP9Jg8I75gXXVW/5fiDkdBmoSiAymEMKBX7D8zZGey/YNHB[/tex]对于式 ( 原)，关于[tex=0.571x0.786]ZKO2xs0EgSemzoH7MSmYTA==[/tex]再求偏导数，则[tex=23.0x2.214]rVglaBLQ7jMj13v2x8A/Pm8x0HZFgW49G7zx6KqqIaDQx3iUPsnqiiLPvYfHYxKF6HA3JkwR/swEGt8b4EBEkDGxj4BhIujCANqK4TwmbUA1uSLLE0bK93GayviXnKfS3SLnmhmXGWJDCc08zxV7gh8jeVMJe8DQkFjPSG9Zp9G2rtxtK1qOC+KRz2Z0UukWvBR6CiskSVUIq9Ionsld++JQ0SLC7oT2QhX45IbxU1FjgPVEAlwTk5E8dVFYenMKIgSR5zogB2CpyFGj0Ks97jWGVH/TlEWZHzy4kmme+swC9F+upAIBWXLXqjyTGq5BQsp5yjnZktpmOlMknaSCePqalE4Rv3NBM0HypAnML+hdsEBcUvG5/2X1n4GASpJU[/tex]于是[tex=14.643x2.929]J0/e9C3IKhr09rvYm0qwksFYgKHlQvs+2VKerE98xZ/qNkanpCmGdbwlFzurDHK0Ux6TvAxmq83oPid/Y1WMCO7m93U8csl+DLWXxMttnjz3VNCwgWSR0zx416DcZOSUVGhpmyFUPEfG/x5YwngfuWUwjXM6bN3PjDBR2lKTj5AoHMbU5n3japnef79k3WCtljhBf9ZQpqzqqiyIsNTAMH5m8ll/NT5gOvIRXfHSc3wW7JCqSWvuMmjjd78WfyMk[/tex][tex=14.714x3.071]6Hi4qRri1Xfrh2DDUsCqIOUCOreCizqJIKUQaxChcE8eAKecIbzEQ+toMzioZR27++1Y3Q9Ktn7YWkyxkWk4K/rEiCMTpvfRUCdN7aD/E3bVbJzOfCq+Te0eIWGyzdjT3gihX+ntA5PzoB7Y1n1L74NAfBhPUHpwNBWsVh3KgC4KAW9wY6ETf8JVsJOrSKExRJNt1xnB61960z2aPyUJKI1h9SV0jmkDPoNuOhmyTcNkPmACEWc5Tp3Gi0zqC0Adkrlyb3UhoLWYLFUB42ZFozh+YHCnxWc1OzRWwcQJ8hg=[/tex]

举一反三

内容

0
设[tex=3.143x1.357]ee8UVMi6ncRcyeiuuPl14g==[/tex]是由方程[tex=5.0x1.429]sIouXO4/kHoUDSOoiuO5xlIz6dhtMgd5HANJh8m9HvE=[/tex]确定的隐函数, 求[tex=1.357x1.214]U9FCP4whLfFgrw52atWKMw==[/tex]
1
求下列方程所确定隐函数的导数：设[tex=5.929x1.357]fA04GAwNKPEexR5aOQYUZQ==[/tex]，求[tex=0.786x1.357]aWqhlS7dEw/6SaOkiRrfqw==[/tex].
2
设方程[tex=4.0x1.214]NARjXYv/ve/pon4punRbag==[/tex] 所确定的隐函数为[tex=3.143x1.357]ee8UVMi6ncRcyeiuuPl14g==[/tex], 求 [tex=2.786x1.429]UHTyjMBYwFmhYt+uhSDHn60CzpIM4SV5igcH0kOUXXk9P5DWXYlEFBq85nzLqjnS[/tex]
3
设4阶行列式[tex=8.643x4.786]kCqzrKR+UWkjw9qkP+VysJkXZPW4gGy3WQYxeVBjPyscbkh4jaqeuzTHKb8ADzZillEJv//dDYsA3eIgtl1m/nm9OC7iB1bU2mKbtX9y2U+l+hgZ+eGWwjw5nXaWh08GIKETM5w8LxpwKqz3U8YNoNCZ5N3cNaZXoyN7V8Cd6/8=[/tex]，求[tex=9.786x1.286]ZzzqfAYue2NjktxDTXMzCBfMGki0q7fbkxRSW9V8r5u5UHngG2n2H+IYF6KiCpGl[/tex] .
4
设方程 [tex=5.143x1.214]DxApH/4cr6s7aDMDl+G+Hw==[/tex] 确定了隐函数 [tex=3.143x1.357]bz5I/Oph6bq+Wf+I30oZgA==[/tex] . 求 [tex=2.143x1.429]aukmIQEmdwJwrrV/0NhREA==[/tex] 及 [tex=2.071x1.429]nbn7ie+LQJlGBJGf1neh2w==[/tex] .