Show that the vector field given is conservative and find its potential function.
F(x, y, z)= (6x^2+4z^3)i +(4x^3y+4e^3z)j + (12xz^2+12ye^3z)k.
The Attempt at a Solution
When I take partial derivative with respect of y for (6x^2+4z^3) and partial derivative with respect of x (4x^3y+4e^3z) they are not equal, then is not conservative. I don't need to check the rest of them , b/c if one fail then it's not concervative.
What about the potential function? I don't think i have to do anything any more in this problem.
I will appreciate any help. Thank you.