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高数求解答?
1个回答
展开全部
∂z/∂x = 2u(∂u/∂x)lnv + (u^2/v)∂v/∂x
= (2u/y)lnv + 3u^2/v = (2x/y^2)ln(3x-2y) + (3x^2/y^2)/(3x-2y)
∂z/∂y = 2u(∂u/∂y)lnv + (u^2/v)∂v/∂y
= (-2xu/y^2)lnv - 2u^2/v = (-2x^2/y^3)ln(3x-2y) - (2x^2/y^2)/(3x-2y)
= (2u/y)lnv + 3u^2/v = (2x/y^2)ln(3x-2y) + (3x^2/y^2)/(3x-2y)
∂z/∂y = 2u(∂u/∂y)lnv + (u^2/v)∂v/∂y
= (-2xu/y^2)lnv - 2u^2/v = (-2x^2/y^3)ln(3x-2y) - (2x^2/y^2)/(3x-2y)
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