grad f(r) Watch

b_t_89
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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
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Kolya
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f is \mathbb{R} \to \mathbb{R} ^n ?
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b_t_89
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it doesnt say
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generalebriety
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(Original post by 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.
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b_t_89
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right...
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Kolya
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(Original post by generalebriety)
Huh? It can't be, the domain of grad is R.
You are right. Sorry.
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b_t_89
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i dont quite get the start of it
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generalebriety
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(Original post by 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?
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rrr99
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how do you use the chain rule for this situation I don't quite understand what you mean
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rrr99
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(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???
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DFranklin
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(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.
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PriyamGhosh
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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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