# Find ∇||r||

• Feb 1st 2013, 08:04 PM
happymatthematics
Find ∇||r||
Hello.
How to find ∇||r||, r=xi +yj +zk
.
My first step:
||r||^2 = rr
then don't know how to continue.

• Feb 1st 2013, 09:13 PM
chiro
Re: Find ∇||r||
Hey happymatthematics.

Hint: Note that in R^3, r.r = x^2 + y^2 + z^2. With grad = (d/dx,d/dy,d/dz) you need to apply each differential operator to ||r|| to get the answer. (Think about differentiating SQRT(x^2 + y^2 + z^2) with respect to each variable).
• Feb 1st 2013, 09:45 PM
happymatthematics
Re: Find ∇||r||
Attachment 26811
I've tried the method you told me, but
haha, My teacher required us to use suffix notation.
Can you teach me how to solve this problem with suffix notation?
• Feb 1st 2013, 09:48 PM
chiro
Re: Find ∇||r||
The RHS will be ||r||^2 = x^2 + y^2 + z^2.
• Feb 1st 2013, 09:54 PM
happymatthematics
Re: Find ∇||r||
but how to represent ||r||^2 = x^2 + y^2 + z^2 in suffix notation?
or how to find ∇||r|| using suffix notation?
• Feb 1st 2013, 10:04 PM
chiro
Re: Find ∇||r||
Do you mean differentiating in terms of d/d||r||? If this is the case you need to use the chain rule where ||r|| = f(x,y,z) and then link d/dr to d/dx, d/dy, and d/dz.

Remember that d/dr(r^2) = 2r.
• Feb 1st 2013, 10:11 PM
happymatthematics
Re: Find ∇||r||
Is d/dr ||r|| = ∇||r|| ?
and is d/dr (rr) = ∂i (ri ri) ?

• Feb 1st 2013, 10:25 PM
chiro
Re: Find ∇||r||
I may agree with you but I have to ask what your definition of r is with respect to the derivative (and also how you link r with x,y,z in terms of the derivatives and the chain rule)?
• Feb 1st 2013, 10:32 PM
happymatthematics
Re: Find ∇||r||
r=(x,y,z)
but can I use r (a vector) to be a variable in differentiation?
d/dr seems strange
• Feb 1st 2013, 10:38 PM
chiro
Re: Find ∇||r||
You can, but you have to define the mapping.

It may not seem intuitive but all that is happening is that you are dealing with a multi-variable situation that is mapping things between elements of a vector.

With the grad operator you have a vector definition (d/dx,d/dy,d/dz) and you are simply mapping things to different elements of a vector.

The general derivative operator for a multi-variable scenario is just a matrix of derivatives which also happens to be a linear object.
• Feb 1st 2013, 10:42 PM
happymatthematics
Re: Find ∇||r||
I've asked my classmate and she said the professor will send us the solution tomorrow. haha.
Thank you chiro.