I'm doing partial derivatives and was wondering if the "yz" in this equation is considered a constant and goes to zero or if just stays the same when derived? Here is the equation:
f(x,y,z)= yz ln (xy)

Question

I'm doing partial derivatives and was wondering if the "yz" in this equation is considered a constant and goes to zero or if just stays the same when derived?  Here is the equation:
f(x,y,z)= yz ln (xy)

anonymous · Answer

If you were diferentiating with respect to x then it would be zero.  If you were diferentiating with respect to y then it would just be z.  If you were diferentiating with respect to z then it would just be y.  In partial derivatives you assume that everything you are not differentiating with respect to is a constant.

As a side not when you find the differential with respect to y you will have to use the product rule because it is present in both terms.