Partial Derivative Question

1. Jul 29, 2011

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

hy = (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?

2. Jul 29, 2011

Dick

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

3. Jul 30, 2011

HallsofIvy

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

4. Jul 30, 2011