令u=x^3+3y^2
du/dx=3x^2
du/dy=6y
则z=f(u)
dz/dx=dz/du*du/dx=f'(u)*3x^2
dz/dy=dz/du*du/dy=f'(u)*6y
d^2z/dx^2=d(dz/dx)/dx=f'(u)*6x+f''(u)*3x^2*3x^2=f'(u)*6x+f''(u)*9x^4
d^2z/dxdy=d(dz/dx)/dy=f''(u)*6y*3x^2=f''(u)*18x^2*y
综上所述，
d^2z/dx^2=f'(x^3+3y^2)*6x+f''(x^3+3y^2)*9x^4
d^2z/dxdy=f''(x^3+3y^2)*18x^2*y
两种方法～一种是设中间变量～一种是不设
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