(6)求 f(x,y)=x/√(x^2+y^2)的偏导数
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f(x,y) = x/√(x^2+y^2) = x(x^2+y^2)^(-1/2)
∂f/∂x = (x^2+y^2)^(-1/2) - (1/2)x(x^2+y^2)^(-3/2) (2x)
= (x^2+y^2)^(-1/2) - x^2(x^2+y^2)^(-3/2) = y^2/(x^2+y^2)^(3/2)
∂f/∂y = - (1/2)x(x^2+y^2)^(-3/2) (2y) = -xy/(x^2+y^2)^(3/2)
∂f/∂x = (x^2+y^2)^(-1/2) - (1/2)x(x^2+y^2)^(-3/2) (2x)
= (x^2+y^2)^(-1/2) - x^2(x^2+y^2)^(-3/2) = y^2/(x^2+y^2)^(3/2)
∂f/∂y = - (1/2)x(x^2+y^2)^(-3/2) (2y) = -xy/(x^2+y^2)^(3/2)
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