# Homework Help: Multivariable Calculus Question involving gradients

1. Feb 24, 2010

### joemabloe

1. The problem statement, all variables and given/known data
Show that $$\nabla$$(r^n)=nr^(n-2)r if n is a position integer.
(hint:use $$\nabla$$(fg)=f$$\nabla$$g+g$$\nabla$$f)
2. Relevant equations

let r(x,y,z) = xi+yJ+zK be the position vector and let r(x,y,z)= |r(x,y,z)|

3. The attempt at a solution

I tried separating $$\nabla$$(r^n) to $$\nabla$$(r^(n-1)*r)

but I can't figure it out.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 24, 2010

### netheril96

I think you may try mathematical induction