Question

z=f[&(x)-y,x+@(y)],f有二阶连续偏导数,&（x） ,@（y)均可导,求二阶混合偏导数6^2z/6x6y

Answer 1

你的符号不习惯,改改：

z = f[g(x)-y,x+h(y)],

则

Dz/Dx = f1*g'(x)+f2*1 = f1*g'(x)+f2,

D²z/DxDy = (Dz/Dx)[f1*g'(x)+f2]

= [f11*(-1)+f12*h'(y)]*g'(x)+f21*(-1)+f22*h'(y)

= -f11*g'(x)+f12*[h'(y)-1]+f22*h'(y).

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