If u=f(y-z, z-x, x-y), then u_{x}+u_{y}+u_{z}

pancha3

pancha3

Answered question

2021-09-16

If u=f(y-z, z-x, x-y), then ux+uy+uz=

Answer & Explanation

gotovub

gotovub

Skilled2021-09-17Added 98 answers

Step 1
Let p=y−z, q=z−x and r=x−y
Now determine the partial derivatives.
px=0,py=1
Similarly
qy=0,qz=1,rz=0andrx=1
Now
ux=uppx+urrx
=1
Step 2
Similarly
uy=uppy+uqqy
=1
uz=uqqz+urrz
=1+0
=1
Therefore
ux+uy+uz=1+1+1
=3
Therefore ux+uy+uz=3
Jeffrey Jordon

Jeffrey Jordon

Expert2022-02-01Added 2605 answers

Answer is given below (on video)

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