Let u=f(r) and r=|x|=((x1)^2 +···|(xn)^2)^1/2.

Question

Show that􏰀 ∑ (∂u/∂xj)^2 = (f′(r))^2

Please help! it's an assignment due tomorrow

Answer 1

Think about this:

u^2 = r^2
2u u' = 2r r'

u^2 = ∑ x_j^2
2u du = 2∑ x_j