同济大学第六版高等数学上下册课后习题
答案8-4
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习题8?4
1? 设z?u2?v2? 而u?x?y? v?x?y? 求?z? ?z?
?x?y 解 ?z??z??u??z??v?2u?1?2v?1?2(u?v)?4x?
?x?u?x?v?x ?z??z??u??z??v?2u?1?2v?(?1)?2(u?v)?4y?
?y?u?y?v?y 2? 设z?u2ln v? 而u?x? v?3x?2y? 求?z? ?z?
?x?yy 解 ?z??z??u??z??v
?x?u?x?v?x221u2x3x ?2ulnv???3?2ln(3x?2y)?? yvy(3x?2y)y2 ?z??z??u??z??v
?y?u?y?v?y222xu2x2x ?2ulnv?(?2)?(?2)??3ln(3x?2y)?? 2yvy(3x?2y)y 3? 设z?ex?2y? 而x?sin t? y?t3? 求dz?
dtdy 解 dz??z?dx??z??ex?2ycost?ex?2y?(?2)?3t2
dt?xdt?ydt ?ex?2y(cost?6t2)?esint?2t(cost?6t2)?
4? 设z?arcsin(x? y)? 而x?3t? y?4t3? 求dz?
dtdy1?12?3??12t 解 dz??z?dx??z?? 22dt?xdt?ydt1?(x?y)1?(x?y)3(1?4t2) ?? 321?(3t?4t)仅供学习与交流，如有侵权请联系网站删除 谢谢9
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5? 设z?arctan(xy)? 而y?ex? 求dz?
dxyex(1?x)dyxdz?z?zx 解 ????? ??e?222222x1?xedx?x?ydx1?xy1?xy
eax(y?z) 6? 设u?2? 而y?asin x? z?cos x? 求du?
a?1dxdy 解 du??u??u???u?dz
dx?x?ydxdzdxaxaeax(y?z)eaxe?2?acosx?2?(?sinx) ?2a?1a?1a?1axe ?2(a2sinx?acosx?acosx?sinx)?eaxsinx? a?1?v? 7? 设z?arctanx? 而x?u?v? y?u?v? 验证?z??z?u?u?vu2?v2y?y?y 证明 ?z??z?(?z??x??z?)?(?z??x??z?)
?u?v?x?u?y?u?x?v?y?v ?1?1?1?(?x)
2xxy2y21?()1?()yy1?1?1?(?x)?(?1)
2xxy2y21?()1?()yy ?2y?v? ?22?ux?yu2?v2 8? 求下列函数的一阶偏导数(其中f具有一阶连续偏导数)? (1) u?f(x2?y2? exy)?
解 将两个中间变量按顺序编为1? 2号?
仅供学习与交流，如有侵权请联系网站删除 谢谢9
最新同济大学第六版高等数学上下册课后习题答案8-4
