Finding Derivatives with the Multivariable Chain Rule

[Doug_West]

Homework Statement

Let f be a differentiable function of one variable, and let
z = f(x + 2y). Show that
2∂z/∂x − ∂z/∂y = 0

Homework Equations

Multi-variable chain rule

The Attempt at a Solution

I have no idea where to start with this, any advice would be greatly appreciated.

Thanks in advance,
Doug

 

[Dick]

Homework Statement

Let f be a differentiable function of one variable, and let
z = f(x + 2y). Show that
2∂z/∂x − ∂z/∂y = 0

Homework Equations

Multi-variable chain rule

The Attempt at a Solution

I have no idea where to start with this, any advice would be greatly appreciated.

Thanks in advance,
Doug

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

 

[Doug_West]

would it be f'(g(x,y))*1?

 

[Dick]

would it be f'(g(x,y))*1?

Yes! Now do ∂z/∂y.

 

[Doug_West]

f'(g(x,y)))*2

 

[Dick]

So 2∂z/∂x − ∂z/∂y equals what?

 

[Doug_West]

0! Thanks for the help.

Doug.