求下列函数的一阶偏导数，其中 [tex=0.5x1.214]gNOHIx2AGu3qP//Yn7oxrg==[/tex]可微：[tex=6.714x1.357]0yrbQ/iXuUhUL2DAgIyzmITLKQ4+j3yCf1bEGC0Z3G4=[/tex]

2022-06-03

求下列函数的一阶偏导数，其中 [tex=0.5x1.214]gNOHIx2AGu3qP//Yn7oxrg==[/tex]可微：[tex=6.714x1.357]0yrbQ/iXuUhUL2DAgIyzmITLKQ4+j3yCf1bEGC0Z3G4=[/tex]

答案：

令[tex=8.0x1.143]mlkj3sP7xoMMrnbVLM1G3pM8T0gCkfjnujrE9sgS/pM=[/tex], 则[tex=5.071x1.357]mypj1gD+E/BBDnlO3yG0+w==[/tex].[tex=28.714x2.429]9tO/e5DyKRkzg0MpCtFEorxsYgY9NTXGHrOpUXmjFzFiXfg7yhlUhkr+CXw9pSoQ97BS5bASsg88Z1Ork48ZOPSQZFjl1Pr8rUpj2QDleqTFB/KKX9dLaKPtskvVoAN8IUR2L1JKPCM+pO2mo/rWqOw/NZRyo0l+82EamPFX8YY77GN9dQ4rdhX8uiYBgWHehZCC6BipWrxgYZj+K93kO8v8donxYeqnFM1KuHSW8/gMNr1q76r+Ib4c6ysRfwEkRBuaDdJ4FphlzcVtsVxZ8l03GvK8Uz3nQvUx/1NpB97I6GGkH8PGO1XCCdLTkPyaPWRzdHIOI4E7DY/DrrBMgW5l1LrVzw4MKgIZMdmE/sxEJ4NTPQ9hv+D6HYzw07eOWHCx2qYQREEB0bmiI5xdRTwiIhtzNwAWCX+pPf1tyk/eWRBWeSY3CspuHFGfWo1+KzB/lPhnqtTFZNaENga4oQ==[/tex][tex=27.286x2.643]9tO/e5DyKRkzg0MpCtFEovUHERrDwGAZ3zsFruAmMrnutkXotXAZywsiwuPJDCIPlz7W8C4KtrLYMpdR+o14xHK+4lGRknRJmzhhc9iAgrFtYXZmC/1JAjMZqsbSc/dlbau+/pbyEJ5vqVQRmwmlgXpcMmG8jBlQQeUIlce2ajoF6jqIqrp+YSgFOFo5QboYE+UkcMekMAtF+jzxThJwlpZQMd8TTyBd7WvvwTow2R5Ai/JKE0Mb6Ow5RbSeNQ9aAiMEepUSDMX5haQuJ4tpksk9w+LKIgXzaicJdtZ+bYKlKz++yBAKQ3VA6V1XcRRowQp5J//Bzr5H/5pX4tTN4i4Q9Kg1MP9y2cgMzOUGa0EHCQRitPdzg2mZ6ZORkhffznGXs8iP2K+WjJHdBmVxpnCm2lFZewOcIGww9lUSiKwLfyzPWq/nYc0xekLbEcc9[/tex][tex=25.071x2.429]9tO/e5DyKRkzg0MpCtFEokknNiQn+QKOD+bOf9GiO8XZwbIBehqskPaK9wXiChVMUnYRXtvF5jnztZtr4/yieRKqktwjS1+0CiPcfyXZf9V0rCuSgCMm2sgRNoc2oTmPH/scznnpONoP12P5qUIG4rz5ybHRuDsMP5b6cN6dJKinZ6yC3xunWoSoX3j5NxHgluN75ZE5hv1PkDKZfckk0tiVMVDi7lEX9Ga3lnv8StWazctnVNRyES7wOdu5yP3DKc9UfmZkXZICdLUTjewNYZlamPFimcRGioQcnzxg9J9eyjgB3eidwWtlu9+eTz2wPFhpuCVVP8cS7E0umSg98H+N6ZjxO/e5/zd/nOL2faiFgAJCLWwefS1rWwsaRSWZCsZg5GaR6B0uT3s984HPrVUvQLf3pxdO7NivRor5t1Y=[/tex]

举一反三

内容

0
求下列函数的一阶偏导数（其中[tex=0.5x1.214]0K9Xf7VHWdVeOrSYAKIm6Q==[/tex]具有一阶连续偏导数）：（3）[tex=6.357x1.357]fQCQ7vHs+rqowuLJLF5hSzjCC9lFaWXA9h//grquBiQ=[/tex]
1
设[tex=0.5x1.214]gNOHIx2AGu3qP//Yn7oxrg==[/tex]为可导函数,求下列各函数的一阶导数：[br][/br](1) [tex=5.571x1.571]h7eWmw/XwEsBN2gkdn2cE9vd8Ve0MATjdsoFxMhCMLFenkwYbbLfP1dxu+eg/tIz[/tex](2)[tex=5.643x1.357]cUjh8uerl905q1pR0g7dPA==[/tex][br][/br]
2
设 [tex=4.714x1.357]qTaybq10oaXkW0nTxPqn6A==[/tex] 其中 [tex=0.5x1.214]gNOHIx2AGu3qP//Yn7oxrg==[/tex] 具有二阶导数，其一阶导数不等于 1, 求 [tex=2.214x2.5]+sfv9fbaljqgKDIK5JrU9TkB7in4U4SOP2zwVb0U7r0=[/tex]
3
设[tex=0.5x1.214]gNOHIx2AGu3qP//Yn7oxrg==[/tex]二阶连续可微,求下列复合函数的偏导数: 设[tex=7.714x1.571]T6UJ67mkjXP3F6fSy13+USIW/T7+jit66ZB0vOrNJjLQNpT+rSbGDH5ZjYDKoNr/[/tex]求 [tex=2.286x2.5]RJakEEAq6IZY8uMTdSFcEHQciZWroG/aWxAiK+JrmCua+s2G0zZBacL72qg4yCt4[/tex]
4
已知[tex=0.5x1.0]wPh71/L+tm8emC/JD+8oZg==[/tex]是可导函数，[tex=0.571x0.786]WLga5RWgrUta8vWDwROpYA==[/tex]为实数，试求下列函数[tex=0.5x1.214]gNOHIx2AGu3qP//Yn7oxrg==[/tex]的导数：[br][/br](1)[tex=7.071x1.357]v21zEkDoMkBc8f7YchBN+oIyy4ANLiyH9hiyIhtvpJA=[/tex]；(2)[tex=7.071x1.357]b9aK1SebpmzwMBC338YzRKzJrljX2jt5U/kV3fSxqik=[/tex]；(3)[tex=6.286x1.357]JxXCGdUuzNxS7ZI7+zEj30kUu/3d3CjqnsqfLf+Y3oU=[/tex]；(4)[tex=6.286x1.357]PW+DAV2BAvZloXe2fXBTQC90pFd/j7+4tQVVKZEn10c=[/tex][br][/br]