Total Differential Problem

[Mechaman]

Here's the problem. Not sure how the first partial dif z/x is set up. why does it become (x+y)(1) - (x-y)(1) / (x+y)^2

Is there a chain rule or product rule being used?

 

[Deleted member 4993]

Here's the problem. Not sure how the first partial dif z/x is set up. why does it become (x+y)(1) - (x-y)(1) / (x+y)^2

Is there a chain rule or product rule being used?

View attachment 4997

While calculating \(\displaystyle \displaystyle{\frac{\partial z}{\partial x}}\)

- y is held constant and then the quotient rule is applied.

Similarly,

while calculating \(\displaystyle \displaystyle{\frac{\partial z}{\partial y}}\)

- x is held constant and then the quotient rule is applied.