证明:若z=x^y(x>0且x≠1),则(x/y)(αz/αx)+(1/ln x)(αz/αy)=2z
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证明:若z=x^y(x>0且x≠1),则(x/y)(αz/αx)+(1/ln x)(αz/αy)=2z
![证明:若z=x^y(x>0且x≠1),则(x/y)(αz/αx)+(1/ln x)(αz/αy)=2z](/uploads/image/z/6688692-36-2.jpg?t=%E8%AF%81%E6%98%8E%EF%BC%9A%E8%8B%A5z%3Dx%5Ey%28x%3E0%E4%B8%94x%E2%89%A01%29%2C%E5%88%99%28x%2Fy%29%28%CE%B1z%2F%CE%B1x%29%2B%281%2Fln+x%29%28%CE%B1z%2F%CE%B1y%29%3D2z)
α是∂吧
z=x^y
∂z/∂x=yx^(y-1)
∂z/∂y=x^y*lnx
(x/y)∂z/∂x+(1/lnx)(∂z/∂y)=(x/y)*yx^(y-1)+(1/lnx)*x^y*lnx
=x^y+x^y=2z
z=x^y
∂z/∂x=yx^(y-1)
∂z/∂y=x^y*lnx
(x/y)∂z/∂x+(1/lnx)(∂z/∂y)=(x/y)*yx^(y-1)+(1/lnx)*x^y*lnx
=x^y+x^y=2z
证明:若z=x^y(x>0且x≠1),则(x/y)(αz/αx)+(1/ln x)(αz/αy)=2z
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