How do u, v, and w relate to the derivatives of x and y?

[kidia]

I need a help on this question,Show that if u=x-y,v=xy and w=f(u,v) then x$$\frac{dw}{dx}$$-y$$\frac{dw}{dy}$$=(x-y)$$\frac{dw}{du}$$.

 

[mathman]

To simplify writing, I will use d for partial derivatives.

f(u,v)=f(x-y,xy)
df/dx=df/du+ydf/dv
df/dy=-df/du+xdf/dv
xdf/dx-ydf/dy=(x+y)df/du

Note difference! (x+y) not (x-y)

 

[Hootenanny]

Suggest moving this to Calc homework pages.

~H

 

[HallsofIvy]

Done! xxxxxxxxx