I am working on an assignment due tomorrow and am just having a hard time with some of this. I think I am on the right track but not sure.

For the first one it wants me to find the four second partial derivatives and observe that the second mixed partial derivaties are equal.

z = ln(x-y) + (x^3)(y^4)

whats throwing me through a loop is taking a deriv of ln(x-y).... the derivative of ln(u) is U' / U

So my first derivs with respect to Y and X would be:

1 - y / (x-y) + (3x^2)(y^4) for diff of z with respect to x

and

x - 1 / (x-y) + (x^3)(4y^3) for diff of z wrt y

if that much is correct I think the rest is but im not sure on that much.

As far as the second goes I'm not sure at all... I will post it in about an hour to an hour and a half. I am in a bind for time right at the moment but wanna use latex and make it proper so I can get some help.

I thank anyone for help in advance.