Question

\[F(x, y, z) = {GmM \over {\sqrt{x^2+y^2+z^2}}}\]
calculate
\[\frac{\partial^2 F}{\partial x^2} + \frac{\partial^2 F}{\partial y^2} + \frac{\partial^2 F}{\partial z^2}\]

Answer 1

do you mean partial derivatives with respect to x^2, y^2, z^2 ?

Answer 2

or is it just 2nd derivatives with respect to x,y,z

Answer 3

yes, I think that notation means take the second derivatives

Answer 4

= 2 ( x² + y² + z²) / √(x² + y² + z²)

Answer 5

I found it 0

Answer 6

it is odd

Answer 7

what do you mean by odd?

Answer 8

strange..

Answer 9

but it coul be thoug..

Answer 10

\[\frac{\partial F}{\partial x} = -\frac{xGmM}{(x^2+y^2+z^2)^{3/2}}\\\frac{\partial^2F}{\partial x^2} = \frac{GmM(2x^2-y^2-z^2)}{(x^2+y^2+z^2)^{5/2}}\]
does this look right?

Answer 11

http://www.wolframalpha.com/input/?i=d^2%2Fdx^2+%28x^2+%2By^2%2Bz^2%29^%28-1%2F2%29%2C+d^2%2Fdy^2%28+x^2+%2By^2%2Bz^2%29^%28-1%2F2%29%2C+d^2%2Fdz^2+%28x^2+%2By^2%2Bz^2%29^%28-1%2F2%29

Answer 12

you are right..

Answer 13

and total is zero..

Answer 14

It says to simplify the answer as much as possible, I guess that 0 will work :)

Answer 15

I found
\[\frac{\partial^2 F}{\partial x^2}=3x^2(x^2+y^+z^2)^{-5/2}-(x^2+y^2+z^2){-3/2}\]
it is the same thing.

Answer 16

your answer is big probably zero..