- #1
wilcofan3
- 27
- 0
Homework Statement
Let [tex]u= (x^2 + y^2 + z^2)^\frac {-1} {2}[/tex]
Find [tex]\frac {\partial^2 u} {\partial x^2} + \frac {\partial^2 u} {\partial y^2} + \frac {\partial^2 u} {\partial z^2}[/tex]
Homework Equations
The Attempt at a Solution
[tex]\frac {\partial^2 u} {\partial x^2} = -(x^2 + y^2 +z^2)^\frac {-3} {2} + 3x^2(x^2 + y^2 + z^2)^\frac {-5} {2}[/tex]
[tex]\frac {\partial^2 u} {\partial y^2} = -(x^2 + y^2 +z^2)^\frac {-3} {2} + 3y^2(x^2 + y^2 + z^2)^\frac {-5} {2}[/tex]
[tex]\frac {\partial^2 u} {\partial z^2} = -(x^2 + y^2 +z^2)^\frac {-3} {2} + 3z^2(x^2 + y^2 + z^2)^\frac {-5} {2}[/tex]
So I think all the partials are right, but I feel like I'm getting a crazy answer when I add them together.
[tex]3x^2 + 3y^2 + 3z^2(x^2 + y^2 + z^2)^\frac {-5} {2} -3(x^2 + y^2 + z^2)^\frac {-3} {2}[/tex]
Is this right?