Can someone help me with the following?

Question

Prove that (grad)^2 f(r) = D^2/dr^2 + (2/r) Df/Dr

Where D^2/dr^2 refers to the second partial derivative of f , w.r.t. r and

Df/ Dr refers to partial derivative of f, w.r.t r

vector r = xi + yj + zk and f(r) is twice differentiable

My work so far :

Definition of grad^2 : (grad)^2 f = fxx+fyy+fzz where the subscripts mean partial derivatives.

For example, fx=∂f/∂x.

r2=x2+y2+z2, so taking partial derivatives of both sides ...

2rrx=2x => rx=x/r and likewise ry=y/r and rz=z/r

Answer 1

what is "D^2/dr^2" ?
It looks like an operator, but ∇²f is not just an operator. Did you mean D^2f/dr^2 ?

Answer 2

Yes, D^2f/dr^2 , thats what I meant there?