Hello.

How to find ∇||r||, r=xi+yj+zk||

.

My first step:

||^2r= r‧r

then don't know how to continue.

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- February 1st 2013, 09:04 PMhappymatthematicsFind ∇||r||
Hello.

How to find ∇||**r**||, r=x**i**+y**j**+z**k**||

.

My first step:

||^2**r****= r**‧**r**

then don't know how to continue.

- February 1st 2013, 10:13 PMchiroRe: 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). - February 1st 2013, 10:45 PMhappymatthematicsRe: 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? - February 1st 2013, 10:48 PMchiroRe: Find ∇||r||
The RHS will be ||r||^2 = x^2 + y^2 + z^2.

- February 1st 2013, 10:54 PMhappymatthematicsRe: 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? - February 1st 2013, 11:04 PMchiroRe: 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. - February 1st 2013, 11:11 PMhappymatthematicsRe: Find ∇||r||
Is d/dr ||r|| = ∇||r|| ?

and is d/dr (**r**‧**r**) = ∂i (ri ri) ?

- February 1st 2013, 11:25 PMchiroRe: 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)?

- February 1st 2013, 11:32 PMhappymatthematicsRe: Find ∇||r||
**r**=(x,y,z)

but can I use**r**(a vector) to be a variable in differentiation?

d/d**r**seems strange - February 1st 2013, 11:38 PMchiroRe: 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. - February 1st 2013, 11:42 PMhappymatthematicsRe: Find ∇||r||
I've asked my classmate and she said the professor will send us the solution tomorrow. haha.

Thank you chiro.

Sorry for wasting your time!!

I think suffix notation is my enemy!! :(

I lack mathematics intuition and inspiration, but I will work hard!