Multivariable Calculus Question involving gradients

[joemabloe]

Homework Statement

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)

Homework Equations

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

The Attempt at a Solution

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

but I can't figure it out.

 

[netheril96]

I think you may try mathematical induction