Задача 32558 3 последнии задачи...

vk34943414

2019-01-05 19:27:37

3 последнии задачи

sova

2019-01-05 19:48:54

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6.4
∂z/∂x=z`_(x)=(1/(x^2+y))*(x^2+y)`_(x)=2x/(x^2+y);
∂z/∂y=z`_(y)=(1/(x^2+y))*(x^2+y)`_(y)=1/(x^2+y).

6.5
gradu=(∂u/∂x)*vector{i}+(∂u/∂y)*vector{i}+(∂u/∂z)*vector{k}

∂u/∂x=(1/(3-x^2))*(3-x^2)`+y^2z*(x)`=(-2x/(3-x^2))+y^2z

∂u/∂y=0 + xz*(y^2)`=2xyz

∂u/∂z=0+xy^2*(z)`=xy^2

gradu=((-2x/(3-x^2))+y^2z)*vector{i}+(2xyz)*vector{i}+(xy^2)*vector{k}


∂u/∂x _(M)=(-2/(3-2^2))+3^2*2=2+18=20

∂u/∂y_(M)=2*1*3*2=12

∂u/∂z_(M)=1*3^2=9

gradu(M)=20*vector{i}+12*vector{i}+9*vector{k}