Tensors: prooving ∇²*r^n

[anaantonia_]

Ok, I have this.

for
$$r = |[B]x[/B]|$$$$[B]x[/B] = x e_1 + x e_2$$
I need to proove:

$$\nabla .(r^n [B]xx[/B])=(n+3)r^n [B]x[/B]$$$$\nabla ^2 r^n = n^{2} r^{n-2}$$$$\nabla ^2 (r^n [B]x[/B])= n(n+2)r^{n-2}[B]x[/B]$$
I tried to do it, but
The in first equation I got n+2
and in the second equation, i can't simplify to it.
Can you help me? *---*

 

[anaantonia_]

Ok, after correcting what I typed, I have this.

for
$$r = |x|$$$$x = x e_1 + x e_2$$
I need to proove:

$$\nabla .(r^n xx)=(n+3)r^n x$$$$\nabla ^2 r^n = n^{2} r^{n-2}$$$$\nabla ^2 (r^n x)= n(n+2)r^{n-2}x$$
I tried to do it, but
The in first equation I got n+2
and in the second equation, i can't simplify to it.
Can you help me? *---*

 

[anaantonia_]

html > me
haha