1)
dz/dx=z*2=2*y^2*e^(2x-y)
dz/dy=z*(2/y-1)=2*y*e^(2x-y)-y^2*e^(2x-y)
d2z/dx2=z*4=4*y^2*e^(2x-y)
d2z/dxdy=2z*(2/y-1)=4*y*e^(2x-y)-2y^2*e^(2x-y)
d2z/dy2=z*(2/y-1)*(2/y-1)-2z/y^2=(2*y*e^(2x-y)-y^2*e^(2x-y))*(2/y-1)-2e^(2x-y)=
=4*e^(2x-y)-2y*e^(2x-y)-2*y*e^(2x-y)+y^2*e^(2x-y)-2e^(2x-y)=
=2*e^(2x-y)-4y*e^(2x-y)+y^2*e^(2x-y)
d2z/dydx=2z*(2/y-1)=d2z/dxdy=4*y*e^(2x-y)-2y^2*e^(2x-y)
2)
dz/dx=2x+(y/x^2)^(1/3)=2*1+(2/1^2)^(1/3)=2+2^(1/3)
dz/dy=-3y^2+(x/y^2)^(1/3)=-3*2^2+(1/2^2)^(1/3)=-12+(1/4)^(1/3)
grad(z)=(2+2^(1/3);-12+(1/4)^(1/3))
(grad(z)*(4;-3))/|(4;-3)| = ((2+2^(1/3))*4+(-12+(1/4)^(1/3))*(-3)) /5 =44/5+4/5*2^(1/3)-3/5*(1/4)^(1/3)
= 9,429961
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расчетов много, проверьте самостоятельно