exact differentials?

Question

Hi-
Show that x^2*y + 3y^2 is an exact differential. I think I am doing this problem right but when I take the partial derivatives they are not equal. Please help!!!!

Answer 1

The criteria for a function to be for an exact differential is that the partial derivative with respect to x is equal to the partial derivative with respect to y.

the derivative with respect to x is:

2xy

the derivative with respect to y is:

x^2 + 6y

It cannot be!, you need to double check the problem.

Answer 2

The exact differential should be in the form:
df = P(x,y)dx + Q(x,y)dy
You are missing the dx and dy.