Question

найти градиент grad u(M) функции u = x^(-2)+3xy^2 в точке M(1;0)

Answer 1

Решение во вложении.

Answer 2

Cпасибо)

Answer 3

$grad, u(x,y)=frac{partial u}{partial x}cdot vec {i}+frac{partial u}{partial y}cdot vec {j}\\u=x^{-2}+3xy^2; ,; ; M(1;0)\\\frac{partial u}{partial x}=-2cdot x^{-1}+3y^2=-frac{2}{x}+3y^2; ,; ; frac{partial u}{partial x}, Big |_{M(1,0)}=-1+0=-2\\frac{partial u}{partial y}=0+3xcdot 2y=6xy; ,; ; ; ; ; frac{partial u}{partial y}, Big |_{M(1,0)}=6cdot 1cdot 0=0\\\grad, u(1,0)=-2cdot vec{i}+0cdot vec{j}=-2cdot vec{i}$