1、_)0,0(,)0,0(),(0)0,0(),(),(2233yfyxyxyxyxyxf求yyxfyyxfyxfyy),(),(lim),(0000000定义：10lim)0,0(),0(lim)0,0(00yyyfyffyyy),(22),(),(lim2)(),(),(lim00bafxbxafbxafxbxbxafbxafxxx的偏导数不变，故是关于,0),(zyzxFFyzFFxzzyxFdyyzdxxzdz隐函数的求导公式：全微分公式：dyzxyzdxzxzdyyzdxxzdzyzyzFFyzyzyzyzyzFFxzyzzxzyxFzyzx)(1ln1ln1)()1(ln1,ln),
2、(2dyxyexyxxzedxxyexyyyzedyyzdxxzdzxyexyxxzeFFyzxyexyyyzeFFxzxyzezyxFdzxyzexyzxyzxyzxyzxyzxyzzyxyzxyzzxxyzxyz1cos1cos1cos1cos6sin),(,6sin解：求已知：221122211211212121)1(1.)1(1.)(1.1.),(yxyxxyzzzyxyxz解：求2221221212)(),(yxffxfyffzyffzxyzxyxfzyxyx解：求已知yyxzzyFFxzyyxzzzFFxzyzzyxFyzxzyzzxzzyzxxzxzxzxlnlnln),(,11
3、1解：求已知：15117)3151(2)(22)1(1.23;102,1,0122512135212421230230ttdttttdtttdxxxtxtxtdtdxtxtxdxxx时，当时，当则解：令页）（课本求：6)43(2arctan211212113,2ln2;1,2ln12),1ln(,11313123122ln22ln222ln22lnxdxxdxxxxedtxtxtdtxxdxxtxeedtttt时当时当则解：令求631arcsin1arcsin1211arcsin21)1(1arcsin1arcsin21arcsin21arcsin21022102221022102210221
4、0221212xdxxxxdxxdxxdxxxxdxxxxdxxxx2ln21)ln2()(lnln11lnlnln1112121111edxxedxxxxxxdxxdxexdxxxdxxeeeeeeee232302332121221103212122110yyyyDxxxxDxdxdyxdxdyxdxdydyxdxdyxdxxdxdy解二：解一：4141412020020202222222yyyyyyDyxxyDyedyedyyedxedydxdyedyedxdxdye解二：难求解一：302322220220222022223,1)(32)(araradrardrraddxdyyxaaaaD
5、152)(61)(01222012dxxxVdxxxSD4sin2sin2sin;4)(2s2dxsinx2dxsinx;00sinxdx2.00000-xdxdxxdxxsxcoinxdx二、3109)6()6()6(|6|432322242442dxxxdxxxdxxxdxxxnnnnnnnln)1(:2)11ln()1(:122111111111111111)1(,13)1(|)1(|,1,11)2()1(|)1(|,1,11)1(11limlim:)(1|)1(|nnnnnnnnnnnnnnnnnnnnnnnnpnpnpppnpnpppppuunpnp条件收敛）（发散发散，故绝对收敛收敛，故比值判别法正项级数先考虑1111)1(141114)(,12)(141224)1(2422232)1ln(12)(2322323222xcxxcdxxxxyxeeexxxQxxxpxxyxxyxyxyxxdxxxdxxpxxxxxxxexxececyyyexxyBAxBAxAyeBAxxyececyrrrr)121()121(1,21,22,)(;2,1,023221221212故通解为非齐次特解为代入原方程：将设非齐次特解为齐次通解为特征根由特征方程31)(3lim31lim)1(lim2202030022理由！（理由！）xxxexdtexxxxtx
