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## Homework Statement

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.

## Homework Equations

## 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.