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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
f is RRn\mathbb{R} \to \mathbb{R} ^n ?
Reply 2
it doesnt say
Kolya
f is RRn\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
right...
Reply 5
generalebriety
Huh? It can't be, the domain of grad is R.
You are right. Sorry.
Reply 6
i dont quite get the start of it
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
how do you use the chain rule for this situation I don't quite understand what you mean
Reply 9
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???
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.
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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