Math Help - Find ∇||r||

1. Find ∇||r||

Hello.
How to find ∇||r||, r=xi +yj +zk
.
My first step:
||r||^2 = rr
then don't know how to continue.

2. 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).

3. Re: Find ∇||r||

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?

4. Re: Find ∇||r||

The RHS will be ||r||^2 = x^2 + y^2 + z^2.

5. 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?

6. 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.

7. Re: Find ∇||r||

Is d/dr ||r|| = ∇||r|| ?
and is d/dr (rr) = ∂i (ri ri) ?

8. 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)?

9. Re: Find ∇||r||

r=(x,y,z)
but can I use r (a vector) to be a variable in differentiation?
d/dr seems strange

10. 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.

11. Re: Find ∇||r||

I've asked my classmate and she said the professor will send us the solution tomorrow. haha.
Thank you chiro.