Question

一道数学偏导数问题求解 感谢！

一道数学偏导数问题求解 感谢！

Answer 1

方向导数等于梯度向量与表示该方向的单位向量的内积

Answer 2

(a) ∂f / ∂x = -y，∂f / ∂y = -x，∂f / ∂z = 3z^2，since P(x,y,z)=(1,1,0)，we have

∇f = ( ∂f/∂x, ∂f/∂y, ∂f/∂z) = (-1, -1, 0)

.

(b) The derivative of f at P in the direction of (1, 1, 1) is

∇f • (1, 1, 1) / |(1, 1, 1)| = (-1, -1, 0) • (1, 1, 1) / (√3) = -2/(√3).