u`_(x)=(yz/x^2)`_(x) + (x/z^4)`_(x) + (z/y^5)`_(x)=
=yz*(x^(-2))`+ (1/z^4)*(x`)+ 0=-2yzx^(-3))+ (1/z^4)
u`_(y)=(yz/x^2)`_(y) + (x/z^4)`_(y) + (z/y^5)`_(y)=
=(z/x^2)*y`+0 +z*(y^(-5))`=
=(z/x^2)-(5z/y^6)
u`_(z)=(yz/x^2)`_(z) + (x/z^4)`_(z) + (z/y^5)`_(z)=
= (y/x^2)*z` +x*(z^(-4))`+(1/y^5)*(z)`=
= (y/x^2) -4x*(z^(-5))+(1/y^5)
M(-2;1;1)
u`_(x)(M)=(-2*1*/(-2)^3))+ (1/z^4)=3/4
u`_(y)(M)=(1/4)-5=-19/5
u`_(z)(M)=(1/4) -4*(-2)*1+(1/1)=37/4
vector{MP}=(0-(-2);0-1;-1-1)=(2;-1;-2)
|vector{MP}|=sqrt(2^2+ (-1)^2+(-2)^2)=sqrt(9)=3
Направляющие косинусы вектора vector{MP}
cos α =2/3
cos β =-1/3
cos γ =-2/3
О т в е т.
u`_(MP)(M)=u`_(x)(M)cos α u`_(y)(M)cos β u`_(z)(M)cos γ =
=(3/4)*(2/3)-(19/5)*(-1/3)-(37/4)*(-2/3) - о т в е т.