Question

решить подробно.помогитееее

Answer 1

dz/dx=(-1/2)x^(-1/2-1)y^(3/2)=-0.5(y/x)^(3/2)
d²z/d²x=(-0.5)(-1.5)y^(3/2)x^(-3/2-1)=0.75y^(3/2)x^(-5/2)
dz/zy=1.5(y/x)^(1/2)
d²z/d²y=1.5*0.5(xy)^(-1/2)=0.75(xy)^(-1/2)
x^2*d²z/d²x=x^2*0.75x^(-5/2)y^(3/2)=0.75x^(-5/2+2)y^(3/2)=0.75x^(-1/2)y^(3/2)
y^2*d²z/d²y=y^2*0.75(xy)^(-1/2)=0.75x^(-1/2)y^(2-1/2)=0.75x^(-1/2)y^(3/2)
вычитая два последних равенства получим 0