Need Help Solving these problems of Partial Differentiation

1.\large 1. GIVEN: F(v2x2,v2y2,v2z2)=0\large F(v^2-x^2,v^2-y^2,v^2-z^2)=0

where v\large v is a function of x,y,zx,y,z

SHOW THAT:\textbf{SHOW THAT:} 1xvx+1yvy+1zvz=1v\large \frac{1}{x}\frac{\partial v}{\partial x}+\frac{1}{y}\frac{\partial v}{\partial y}+\frac{1}{z}\frac{\partial v}{\partial z}=\frac{1}{v}

2.\large 2. GIVEN: V=f(X,Y,Z) V=f(X,Y,Z) is a homogeneous function in x,y,zx,y,z of degree n\boxed{n}

where X=Vx,Y=Vy,Z=Vz X=\dfrac{\partial V}{\partial x}, Y=\dfrac{\partial V}{\partial y}, Z=\dfrac{\partial V}{\partial z}

SHOW THAT:\textbf{SHOW THAT:} XVX+YVY+ZVZ=nn1V\large X\frac{\partial V}{\partial X}+Y\frac{\partial V}{\partial Y}+Z\frac{\partial V}{\partial Z}=\frac{n}{n-1}V


Now for the second one, i understand that the Euler's theroem is necessary but i can't proceed in a definite direction from there

Note by Aritra Jana
2 years, 11 months ago

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@Aritra Jana sorry but I don't know much about partial derivatives.

Parth Lohomi - 2 years, 11 months ago

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oh sorry, my bad. although , could you help me by tagging some who you think have a certain degree of knowledge in this field?

Aritra Jana - 2 years, 11 months ago

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@Otto Bretscher

Parth Lohomi - 2 years, 11 months ago

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What have you done? What have you tried?

Can you show your working?

Calvin Lin Staff - 2 years, 11 months ago

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@Aritra Jana @Calvin Lin i am opening brilliant after 3 years. i think i have 2 solutions to problem 1 but i am not being able to post a picture.plz help

Arkajyoti Maity - 2 years, 7 months ago

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Approaches

  1. If you email it to me, I can upload it for you.
  2. If you upload it to an image site like Imgur, you can then use the markedown syntax of ![](URL) to display images.

Calvin Lin Staff - 2 years, 7 months ago

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