设z=y/xf(xy)+yg(x2+y2),其中f,g二阶连续可导,则

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问题 设z=y/xf(xy)+yg(x2+y2),其中f,g二阶连续可导,则

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答案1/2edx-1/2dy

解析 dz/dx=y/x2f(xy)+y2/xf’(xy)+2xyg’(x2+y2),d2z/dxdy=-1/x2f(xy)+y/xf’(xy)+y2f"(xy)+2xg’(x2+y2)+4xy2g"(x2+y2).
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