# Gradient of an absolute value raise to a power

1. Mar 17, 2013

### Estane

1. The problem statement, all variables and given/known data

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

x and y are vectors.

2. Relevant equations

3. 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

Last edited: Mar 17, 2013
2. Mar 17, 2013

### SammyS

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