Find the gradient vector field vec F = grad f for each of the function f(x,y,z)=sqrt(x^2+y^2+z^2)

glasskerfu

glasskerfu

Answered question

2020-10-28

Find the gradient vector field F=f for each of the function f(x,y,z)=x2+y2+z2

Answer & Explanation

Corben Pittman

Corben Pittman

Skilled2020-10-29Added 83 answers

F<fx,fy,fz
fx=xx2+y2+z2=12x2+y2+z212(2x)=xx2+y2+z2
fy=yx2+y2+z2=12x2+y2+z212(2y)=yx2+y2+z2
fz=zx2+y2+z2=12x2+y2+z212(2z)=zx2+y2+z2
Therefore,
F<xx2+y2+z2,yx2+y2+z2,zx2+y2+z2>

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