grad f(r)

I have to find

\bigtriangledown

f(r), where r= |r|, r=(x,y,z) and f is a differentiable function, and answer to be expressed in terms of r.

Does anyone know where to start here? Thanks

Reply 1

Kolya

f is

\mathbb{R} \to \mathbb{R} ^n

Reply 2

b_t_89

it doesnt say

Reply 3

generalebriety

Kolya

f is

\mathbb{R} \to \mathbb{R} ^n

Huh? It can't be, the domain of grad is R.

Well, grad f(r) is (df(r)/dx, df(r)/dy, df(r)/dz). However, r is sqrt(x^2 + y^2 + z^2). Use the chain rule so that the terms look like df/dr * dr/dx, then take out the common factor of df/dr. Finally, evaluate what's left by putting r = sqrt(x^2 + y^2 + z^2) and rewriting the whole thing in terms of r.

Reply 4

b_t_89

right...

Reply 5

Kolya

generalebriety

Huh? It can't be, the domain of grad is R.

You are right. Sorry.

Reply 6

b_t_89

i dont quite get the start of it

Reply 7

generalebriety

b_t_89

i dont quite get the start of it

That's not helpful. Can you tell me what precisely you don't understand?

Reply 8

rrr99

how do you use the chain rule for this situation I don't quite understand what you mean

Reply 9

rrr99

Original post by generalebriety

That's not helpful. Can you tell me what precisely you don't understand?

how do you use the chain rule in this situation ?? because r is a variable of function f how do you change that???

Reply 10

DFranklin

Original post by rrr99

how do you use the chain rule for this situation I don't quite understand what you mean

Thread is 10 years old.

Reply 11

PriyamGhosh

Actually f is the function of r. And when the variables of a vector is not mentioned we use the generalized variables, i.e., (x,y,z) {the cartisian coordinates}.

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