Using Multi-Variable Chain Rule to Prove Equation Involving z = f(x^2 + y^2)

[hangten1]

Homework Statement

z = f (x^2 + y^2)
prove using multi var chain rule that

y * dz/dx - x * dz/dy = 0

Homework Equations

The Attempt at a Solution

honestly i just need to no how to start it then I am sure i could figure the rest out

so i would find dz/dx and dz/dy then what would x and y be? and do i substiude any values of x and y to prove it works?

 

[Doug_West]

z=f(g(x,y)), where g(x,y)=x^2+y^2. Now what does the chain rule tell you about, say ∂z/∂x?

 

[hangten1]

something like dz/dx = dz/dg dg/dx?

(d = that stupid partial sign)

 

[SammyS]

something like dz/dx = dz/dg dg/dx?

(d = that stupid partial sign)

If you use the "Go Advanced" button below the message box, then you have a new message box with a set of symbols on the right. Find the stupid ' ∂ ' there !

 

[Dick]

something like dz/dx = dz/dg dg/dx?

(d = that stupid partial sign)

f is a function of one variable. You could also write ∂z/∂g as f'(g(x,y)). Now what's ∂g/∂x?

 

[hangten1]

2x * 1?

 

[ehild]

Yes.

ehild

 

[hangten1]

tys dick and ehild

think i got it