Задача 65071 ФМП: u=(x^3)+(2y^2)-(4z^5)+xcos2z du/dx,...

62a70ccc50cfaa3742022379

13.06.2022 21:03:23

ФМП: u=(x^3)+(2y^2)-(4z^5)+xcos2z
du/dx, du/dy, du/dz, (d^2)u/dxdz

5f3ea7e3faf909182968ddd9

13.06.2022 22:05:38

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[m]u=x^{3}+2y^2-4z^5+x\cdot cos2z[/m]

[m]\frac{ ∂ u}{ ∂ x}=u`_{x}=(x^{3}+2y^2-4z^5+x\cdot cos2z)`_{x}=3x^2+cos2z[/m]


[m]\frac{ ∂ u}{ ∂ x}=u`_{y}=(x^{3}+2y^2-4z^5+x\cdot cos2z)`_{y}= 4y [/m]


[m]\frac{ ∂ u}{ ∂z}=u`_{z}=(x^{3}+2y^2-4z^5+x\cdot cos2z)`_{z}=-20x^4-2xsin2z [/m]


[m]\frac{ ∂^2 u}{ ∂ x ∂z }=(u`_{x})`_{z}=(3x^2+cos2z)`_{z}=(-sin2z)\cdot (2z)`=-2sin2z[/m]