Multi variable partial differentiation, cant solve

[LovePhysics]

Homework Statement

If z = f(x-y), show that dz/dx + dz/dy = 0

2. The attempt at a solution
I thought:

dz/dx = fx
dz/dy = -fy

which doesn't make sense really... because its not equal to 0.

or maybe it should be:
dz/dx = dz/df * df/dx = fx * ??
dz/dy = dz/df * df/dy = -fy * ??

 

[HallsofIvy]

Homework Statement

If z = f(x-y), show that dz/dx + dz/dy = 0

2. The attempt at a solution
I thought:

dz/dx = fx
dz/dy = -fy

which doesn't make sense really... because its not equal to 0.

or maybe it should be:
dz/dx = dz/df * df/dx = fx * ??
dz/dy = dz/df * df/dy = -fy * ??

Use the chain rule. If z= f(u) and u= x- y then $\partial f/\partial x= df/du \partial u/\partial x$ and $\partial f/\partial y= df/du \partial u/\partial y$.

(If z= f, then "dz/df" is just 1.)

 

[LovePhysics]

Use the chain rule. If z= f(u) and u= x- y then $\partial f/\partial x= df/du \partial u/\partial x$ and $\partial f/\partial y= df/du \partial u/\partial y$.

(If z= f, then "dz/df" is just 1.)

Thats great thx.

dz/dx = df/du du/dx = fu * 1 = fu
dz/dy = df/du du/dy = fu * -1 = -fu


dz/dx + dz/dy = fu - fu = 0