z=(x+y)/(x-y) dz=?已知[(x+ay)dx+(ax+y)dy]/(x+y)²

z=(x+y)/(x-y) dz=?已知[(x+ay)dx+(ax+y)dy]/(x+y)²

z=(x+y)/(x-y) dz=?已知[(x+ay)dx+(ax+y)dy]/(x+y)²为某一二院函数的全微分,a=?已知（axy³-y²cosx)dx+(bysinx+3x²y²)dy为f(x y)的全微分,ab的值(图1)答案网 www.Zqnf.com 答案网 www.Zqnf.com ======以下答案可供参考======供参考答案1: z=(x+y)/(x-y) dz=?已知[(x+ay)dx+(ax+y)dy]/(x+y)²为某一二院函数的全微分,a=?已知（axy³-y²cosx)dx+(bysinx+3x²y²)dy为f(x y)的全微分,ab的值(图2)供参考答案2:z=(x+y)/(x-y) dz=[(x-y)-(x+y)]/(x-y)^2dx+[(x-y)+(x+y)]/(x-y)^2dy=[-2y/(x-y)^2]dx+[2x/(x-y)^2]dy下面两问有点难，属于已知二元函数的全微分求原函数的表达式，这个需要用格林公式的问题解决，原函数等于它的全微分再积分，你慢慢算吧，不会的话就在网上搜高等数学A下（同济大学版），相关知识在书上的180页到181页。第二题参考楼下的回答。已知（axy³-y²cosx)dx+(bysinx+3x²y²)dy为f(x y)的全微分df(x y)/dx=axy³-y²cosx对x积分f(x y)=(a/2)(x^2)(y^3)-y^2sinxdf(x y)/dy=bysinx+3x²y²对y积分f(x y)=f(x y)=(x^2)(y^3)+(b/2)y^2sinx对应项相等，a=2,b=-2采纳我吧！供参考答案3:dz=fxdx+fydy=[[(x-y)-(x+y)]/(x-y)^2 ]dx+[[(x-y)+(x+y)]/(x-y)^2]dy=-2y/(x-y)^2 dx+2x/(x-y)^2 dy =2/(x-y)^2 (xdy-ydx)由dP/dy=dQ/dx(偏导符号打不出，这里用d代替了）可求出a=1,这时[(x+ay)dx+(ax+y)dy]/(x+y)的平方=dln(x+y).df/dx=axy³-y²cosx........(1)

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