Is Using the Quotient Rule for Partial Derivatives Correct?

[newyorkcity]

For the equation:

h(x,y,z)=y/(x+y+z)

using quotient rule:

f(y)=y
g(x,y,z)=x+y+z

h_y = (x+y+z)(1)-(y)(1) / (x+y+z)²
= x+z / (x+y+z)²

I am getting the correct answer when evaluating at a point, but is this differentiation correct?

More specifically, when using the quotient rule for partial derivatives, is it correct to differentiate f and g with respect to y, and then apply the quotient rule? Is this method generally correct?

 

[Dick]

You are doing just fine. Yes, it is generally correct.

 

[HallsofIvy]

The partial derivative is just the ordinary derivative with the other variables treated like constants. All ordinary derivative laws apply to partial derivatives.

 

[newyorkcity]

Great, thanks for your help.