Question

Найти градиент функции f(x,y)=( -x^3-6*x^2*y-6*x*y^2-3*x*y) в точке М(-4;4)

Answer 1

$f(x,y)=-x^3-6x^2y-6xy^2-3xy\; ,\; M(-4;4)\\\\f'_{x}=-3x^2-12xy-6y^2-3y\\\\f'_{y}=-6x^2-12xy-3x\\\\f'_{x}(-4,4)=-48+192-96-12=36\\\\f'_{y}(-4,4)=-96+192+12=108\\\\\overline {gradf(x,y)}\, |_{M(-4,4)}=36\overline {i}+108\overline {j}$