Gradient of an absolute value raise to a power

[Estane]

Homework Statement

Show that ∇$_{x}$|x-y|^-3= -(x-y)|x-y|^-3

x and y are vectors.

Homework Equations

The Attempt at a Solution

When dealing with just a straight up absolute value I know that a solution can be found by using a piece wise approach, but I don't think that's what I should be using here. The power is throwing me completely and I have no idea how to deal with it.

Thanks

 

[SammyS]

Homework Statement

Show that ∇$_{x}$|x-y|^-3= -(x-y)|x-y|^-3

x and y are vectors.

Homework Equations

The Attempt at a Solution

When dealing with just a straight up absolute value I know that a solution can be found by using a piece wise approach, but I don't think that's what I should be using here. The power is throwing me completely and I have no idea how to deal with it.

Thanks

Yes, the piecewise approach is what you should be using here.

Show us your attempt so we can help you.