Asked by Aryaa
Can someone help me with the following?
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
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
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