设f(x,y,z)=x^2+y^2+z^2,求gradf(1,-1,2)及其模

Question

如题所述

Answer 1

这里打不了偏导符号，将就一下...
df/dx = 2x, df/dy = 2y, df/dz = 2z, gradf = (2x, 2y, 2z), gradf(1, -1, 2) = (2, -2, 4),
|gradf(1, -1, 2)| = |(2, -2, 4)| = sqrt(2^2 + (-2)^2 + 4^2) = sqrt(4 + 4 + 16) = 2sqrt(6)本回答被提问者和网友采纳

Answer 2

gradf(x,y,z)=2xi+2yj+2zk，gradf(1,-1,2)=2i-2j+4k；模|gradf((1,-1,2)|=2√6。