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Multivariable & Vectorhard
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Let f(x,y)=x3−2x2y+3xy2f(x, y) = x^3 - 2x^2y + 3xy^2f(x,y)=x3−2x2y+3xy2 (homogeneous of degree 3). According to Euler's theorem for homogeneous functions, if n=3n = 3n=3 is the degree, then x⋅fx+y⋅fyx \cdot f_x + y \cdot f_yx⋅fx​+y⋅fy​ should equal which expression?