Partial Derivatives: Help & Thanks!

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Homework Help Overview

The discussion revolves around the topic of partial derivatives, specifically involving a function f defined in terms of variables u and v, which are expressed as functions of x and y. Participants are exploring the implications of the condition f(u,v) = 0 and the relationship z = g(x,y).

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to calculate the partial derivatives df/dx and df/dy using the chain rule. There are questions about how to link the derivatives to the given conditions and how to substitute the variables correctly.

Discussion Status

The discussion includes attempts to derive equations for the partial derivatives and explore their relationships. Some participants have expressed understanding of the implications of the equations, while others are seeking clarification on the substitution of variables.

Contextual Notes

There is a focus on the condition f(y/x, z/x) = 0, and participants are considering how this affects the derivatives. The discussion also touches on the need for proper substitutions in the context of the problem.

imana41
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please help about this
if f(u,v)=f(y/x,z/x)=0 and z=g(x,y) and
gif.latex?\frac{\partial%20f}{\partial%20v}\neq%200.gif


show
gif.latex?x\frac{\partial%20g}{\partial%20x}+y\frac{\partial%20g}{\partial%20y}=g(x,y).gif


thanks a lot
 
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imana41 said:
please help about this
if f(u,v)=f(y/x,z/x)=0 and z=g(x,y) and
gif.latex?\frac{\partial%20f}{\partial%20v}\neq%200.gif


show
gif.latex?x\frac{\partial%20g}{\partial%20x}+y\frac{\partial%20g}{\partial%20y}=g(x,y).gif


thanks a lot

Can you calculate df/dx and df/dy?
And do you know which value they would take?
 
df/dx = df/du . du/dx + df/dv .dv/dx and lik this for df/dy
 
imana41 said:
df/dx = df/du . du/dx + df/dv .dv/dx and lik this for df/dy

True.

And since f(y/x, z/x) = 0 it follows that df/dx=0 and that df/dy=0.

So if you write out the equations for df/dx and df/dy you have 2 equations that can be solved.
 
20u}{\partial%20y}+\frac{\partial%20f}{\partial%20v}\times%20\frac{\partial%20v}{\partial%20y}=0.gif


but how i linking it to
gif.gif
 
imana41 said:
20u}{\partial%20y}+\frac{\partial%20f}{\partial%20v}\times%20\frac{\partial%20v}{\partial%20y}=0.gif


but how i linking it to
gif.gif

You are forgetting to substitute u=y/x and v=g(x,y)/x
 
thanks i get the answer
the latest symplify is
\frac{\partial%20g}{\partial%20x}\times%20x-g(x,y)}{x\times%20\frac{\partial%20g}{\partial%20y}}.gif


and then
gif.latex?x\frac{\partial%20g}{\partial%20x}+y\frac{\partial%20g}{\partial%20y}=g(x,y).gif
thanks for your help
and another answer is it true
gif.gif
 
Last edited:

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