How to Calculate the Gradient of a Separation Vector?

[starbaj12]

Let c' be the separation vector from a fixed point(x'',y'',z'') to the point (x,y,z) and let c be its length. show that

Gradient(1/c) = -c'(hat)/c^2

Thnaks for the help

 

[cronxeh]

your work?

 

[kkan2243]

begin by writing 1/c in terms of cartesian coordinates.

c = sqrt[(x - x`)^2 + (y - y`)^2 + (z - z`)^2]
1/c = ?

then differentiate using multiple applications of the chain rule. Remember that the primed terms are constant when differentiating respect to x, y or z. This was the part that confused me at the beginning as I didn't know how to differentiate those.

 

[mathwizarddud]

Let c' be the separation vector from a fixed point(x'',y'',z'') to the point (x,y,z) and let c be its length. show that

Gradient(1/c) = -c'(hat)/c^2

Thnaks for the help

What is "hat"?

 

[tiny-tim]

^

What is "hat"?

"hat" is ^

it means the unit vector in the direction of c'