u`_(x)=(z/x^2)`_(x) (xz^2y^3)`_(x) (yz^4)`_(x)=
=z*(x^(-2))` (zy^3)*(x`) 0=-2zx^(-3)) (zy^3)
u`_(y)=(z/x^2)`_(y) (xz^2y^3)`_(y) (yz^4)`_(y)=
=0 xz^2*(y^3)` z^4*(y)`=
=3xz^2y^2 z^4
u`_(z)=(z/x^2)`_(z) (xz^2y^3)`_(z) (yz^4)`_(z)=
= (1/x^2)*z` (xy^3)*(z^2)` y*(z^(4))`=
=(1/x^2) 2xy^3z 4yz^3
M(-1;2;1)
u`_(x)(M)=2*1(-1)^(-3)) (1*2^3)=10
u`_(y)(M)=3(-1)*1^2*2^2 1^4=-11
u`_(z)(M)=(1/(-1)^2) 2*(-1)*2^3*1 4*2*1^3=
=1-16 8=-7
vector{MP}=(3 1;-6-2;2-1)=(4;-8;1)
|vector{MP}|=sqrt(4^2 (-8)^2 1^2)=sqrt(81)=9
Направляющие косинусы вектора vector{MP}
cos α =4/9
cos β =-8/9
cos γ =1/9
О т в е т.
u`_(MP)(M)=u`_(x)(M)cos α u`_(y)(M)cos β u`_(z)(M)cos γ =
=10*(4/9)-11*(-8/9)-7*(1/9)=121/9