# Homework Help: Multivariable chain rule

1. Jan 2, 2012

### hangten1

1. The problem statement, all variables and given/known data
z = f (x^2 + y^2)
prove using multi var chain rule that

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

2. Relevant equations

3. The attempt at a solution

honestly i just need to no how to start it then im 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?

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2. Jan 2, 2012

### 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?

3. Jan 2, 2012

### hangten1

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

(d = that stupid partial sign)

4. Jan 2, 2012

### SammyS

Staff Emeritus
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 !

5. Jan 2, 2012

### Dick

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

6. Jan 2, 2012

2x * 1?

7. Jan 3, 2012

Yes.

ehild

8. Jan 3, 2012

### hangten1

tys dick and ehild

think i got it