设函数[tex=3.143x1.357]Eg6rSgUNTUffRvxyTlFbYQ==[/tex]充分多次可微. 求反函数[tex=4.214x1.5]r2jmw55kMrkPXJAoU7k29A==[/tex]的导数[tex=5.857x1.5]FwhiiH4iUlMuDyjUdwrlAc1wMFZbp7CCbiqKmZcpt1dI9gS5yr8xtxjoEzjiaDUhVHfyqIO3xNzNANguv0Kbi7IdRa14tehWec/DJePH1iU=[/tex](设这些导数都存在）

2022-06-04

设函数[tex=3.143x1.357]Eg6rSgUNTUffRvxyTlFbYQ==[/tex]充分多次可微. 求反函数[tex=4.214x1.5]r2jmw55kMrkPXJAoU7k29A==[/tex]的导数[tex=5.857x1.5]FwhiiH4iUlMuDyjUdwrlAc1wMFZbp7CCbiqKmZcpt1dI9gS5yr8xtxjoEzjiaDUhVHfyqIO3xNzNANguv0Kbi7IdRa14tehWec/DJePH1iU=[/tex](设这些导数都存在）

答案：

解 [tex=18.071x5.643]Ck4j1YFlvVH5wCAykOEMi6oTUnw/ug1RYleslnRxdwpL3HGomgYuE1BsEeBItQ0OihdsIlxnPy9Cmjxy0alzjtdc5pqwVGBj8O2VBcFV4vQTPzlFRR0QYUQ9xUltwZPiF9zkiarXswlEkcY2PNssh5t3oyVGSdgmG1KOgKHPYbshhA4TddV1O7yGt0W9Qla7A/rEk01sEsC37xg0nP/TKHkP8tsiTEoheHl2L0aA2tY/a+8ztLdKNknwTaMB7ICY6evCF4WhdYxOh4g2mbJO3OOaUqb3pokN+trwXerrtkp38SAedFvpac5Dv/hBsbCNixv44G+9FjfamFeAyytQmUf0G/lvb1+SLihJEFCENyq9UzIQOsSFHQ2sQW18C7CFD5kJz5iViYUarQ7Zg75svw==[/tex][tex=19.429x3.0]5N4fE/+TRNVJnPQE2QZxntsc0ZAz3hC5DXex7HbjWXWtzlHrBMFS5yskbEtPGWUNMMzhWVRtTbC8kkAiMCRSb4RgtzkvysyZqcO2Gp+yW0MdOTQd9VXGYTQVZPtXpS9Gw7hDgOgipDJoWLuL6CvWFEF0zXdkFDfj+4dIh6emadrwG7c0xxzXi/hc9DPYno7rIUVf4ivNhtDWIIvbR3gMJoutAVoAEXQ2jTY2WT8Q9shpEz2UqkgwwpW77PeVXs0BJ3IlwwN1N6FDmWD45XmXG2pXIQDEbkrvDoXualkcPqZA4r0yhzNJxIdRsPrpiiOmpFNYe50MNsLDKpSm7Lyr78phMQ98ShiQrtDr8YhtoGEM29MxCvRM1hTrfavuiz3z[/tex][tex=26.571x3.429]nA2SzCabkeNxpGyV/QktgZADwrxCj16alkQniUchWeT1SRzg5pEDmZx82m/+05j70nt4+Eut6ndDeT5rn3Wq+vNl4p31tDlD43JC7Ogio/aFvp8NitmPxjtL7ovOrMWMgDenvc2kyRaZpseDqleHbjYceKamNReZVwXAPDnz3oHbcocL1rWDivDIn556mkWO/BcC//zLwXYxGJE9EMZbJq1RG3v7Ii1g73F8GhlCV1A8tli0F5hBHBERSFdXUZgEGWtJte6dKYX3WhHo0wniaEmR6Zr2Y93ZlNMWnP0F5iXX6dHi+cays4FjwBt0HWoqqA6hrtUviaYf4BWFUnD6QIrq/TIS3HeMHxG+23aenS/lmnZhEkJouO4dnGPN3bl6C9II1DcH5vKZyZptl18EqA6JRCW7fDFgisYShTsNDTJVkZdT5LMwuLHtV0sUBsQ129DI40NKwiejeWD27fxUIQ==[/tex]     [tex=17.214x2.786]f6ApXzR2qLRVungF/Dtr6bQopCo4gjjsvyOZtnqREAinAA+IYvhgWJ+1OVu9iMQk0RL6e+gT8Xl1FjGPA+5ez1ZBUbuJmJgtu9kslOuTlHpGEff6R1WQ3iMFygg4lXhTczVQLSIXaNcuQlQXjR1vsYTKZ1Ogteqi/vOfD/xPJzxTYxtJYil/vT1mRQwEBR3raCgMudTu01g1NemU5eIhWr/DIhqXe0aUPUA1ln66JAI=[/tex]

举一反三

内容

0
设函数[tex=3.143x1.357]Eg6rSgUNTUffRvxyTlFbYQ==[/tex]在点[tex=0.571x0.786]c5VsltFnl9nO0qB/vNKOWA==[/tex]二阶可导，且[tex=4.071x1.429]U93ae75fuTDIyESpUsh0Znxw8HsPs/3+dKg1A7Sgz2g=[/tex].若[tex=1.857x1.357]BGkv0wKMIn2R4tUsMDFEFA==[/tex]存在反函数[tex=4.214x1.5]X4tnRmg9ptWcXRsWJCIE5iFzaBn0AyeVAzDEO7/ylT4=[/tex]，试用[tex=5.0x1.429]U93ae75fuTDIyESpUsh0Zvaxe9NteqcymEPLd1HF4oN74xhsC9JoCG9xIxr00sj6[/tex]以及[tex=2.571x1.429]o1NxfHFvh4pfuP8b7Vf/BLM9mw2a8g13iR+liT0iBJOcTMG5+16J5Iuai7VsI2ee[/tex]表示[tex=4.5x1.643]WfldAP4jTSnBM8Wh+uruUgZBFwSP/ENp0INsrcYyk4n+zScHyfcxFyF9NLgREvygC08tq3NgLA4OzAsJJnzXqg==[/tex]
1
设函数[tex=3.571x1.286]VhM8EK25rb5AWmEItkNOoQ==[/tex]，[tex=3.714x1.286]ILxTGSNsFVqbb4UrB1q2og==[/tex]都存在二阶导数，求复合函数[tex=4.714x1.286]RRs92pK5qkohrd+7xlMNhw==[/tex] 的二阶导数。
2
设函数[tex=6.571x1.5]sE6Aas6x+mULF9vvpSmxZ+FhRWN40wttmb1RYCf053k=[/tex]。(1)求一阶导数[tex=2.214x1.429]iNxCerDUViDWTqUmlPeFSQ==[/tex]；(2)证明[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]在[tex=1.857x1.0]jl8uliKUg6qIeVpZvtGL9Q==[/tex]处不存在二阶导数。
3
设[tex=0.5x1.214]0K9Xf7VHWdVeOrSYAKIm6Q==[/tex]为可导函数，求下列各函数的一阶导数（1）[tex=5.571x1.571]CzOsk6CTm+AeH5u1ClC8Qg54CGvuiOpPKQ7V/SeG0gws0zh00FvMrAnQ5XkPjagU[/tex]
4
设函数[tex=3.571x1.286]VhM8EK25rb5AWmEItkNOoQ==[/tex]，[tex=3.714x1.286]ILxTGSNsFVqbb4UrB1q2og==[/tex] 都存在三阶导数，求复合函数[tex=4.714x1.286]RRs92pK5qkohrd+7xlMNhw==[/tex]的三阶导数[tex=1.786x2.571]4MHhesgJJwrKkcFfvkAG+4yMsw3aD8GpxNcW6Zkrj5VZqTMoEzN6I/RNC/cYNU0g[/tex]。