Let (x, y, z) = ex 2 y 2 z2 = e r2 , with r as

Let ƒ(x, y, z) = e−x^2−y2−z2 = e^−r2 , with r as in Exercise 35. Compute ∇ƒ directly and using Eq. (9).

Data From Exercise 35

Let r = (x, y, z) and e_r =r/ ΙΙrΙΙ. Show that if a function ƒ(x, y, z) = F(r) depends only on the distance from the origin r = ΙΙrΙΙ= √x² + y² + z², then

Transcribed Image Text:

Vf = F'(r)er