Let X be an open set in R n , F: X ⊆ Rn → Rn a vector field on...

Let X be an open set in R ⁿ , F: X ⊆ Rⁿ → Rⁿ a vector field on X, and a ∈ X. If v is any unit vector in Rⁿ, we define the directional derivative of F at a in the direction of v, denoted D_vF(a), by provided that the limit exists. Exercises 31–34 involve directional derivatives of vector fields.

Let F = yz i + xz j + xy k.Find

(Hint: See Exercise 31.)