设函数f(x,y)=x²2xy-yx,则gradf(1,1)=

更新时间2018-12-28 05:25:38

1 若 f(x,y) = x²+2xy-yx

f'x = 2x+2y-y

f'y = 2x-x

故，梯度 grad f(x,y)=(2x+2y-y,2x-x)

grad f(1,1)=(3,1)

2 若 f(x,y) = x²-2xy-yx

f'x = 2x-2y-y

f'y = -2x-x

故，梯度 grad f(x,y)=(2x-2y-y,-2x-x)

grad f(1,1)=(-1,-3)