I am having trouble with two questions, one is with a quotient rule and the other a product rule I believe. Instructions indicate to compute all first order derivatives of the given function.

Z= xe^xy

Here is what I did: fx= (x)(ye^xy) + (e^xy)(1) Is this correct?

I started using the product rule again for (fy) but then I saw an example in the book where they used the constant multiple rule. Why am I supposed to use this rule and not the product rule? The book shows a similar example and they used the product rule to differentiate fx and used the constant multiple rule to differentiate fy, I would just like to know why this is...

My second set of problems is:

1. 2x+3y / y-x

2. e^2-x / y^2

I know the quotient rule can be used, but I was not sure how to keep y and x as constants. If someone can illustrate the steps involved, Thanks...