Partial Derivatives: Help & Thanks!

[imana41]

please help about this
if f(u,v)=f(y/x,z/x)=0 and z=g(x,y) and

show

thanks alot

 

[I like Serena]

please help about this
if f(u,v)=f(y/x,z/x)=0 and z=g(x,y) and

show

thanks alot

Can you calculate df/dx and df/dy?
And do you know which value they would take?

 

[imana41]

df/dx = df/du . du/dx + df/dv .dv/dx and lik this for df/dy

 

[I like Serena]

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.

 

[imana41]

but how i linking it to

 

[I like Serena]

but how i linking it to

You are forgetting to substitute u=y/x and v=g(x,y)/x

 

[imana41]

thanks i get the answer
the latest symplify is

and then

thanks for your help
and another answer is it true