Determine if the given vector field F is conservative or not:
F = (2xyz, sin(xy), 3ez^2)
Conservative: not conservative
If F is conservative, find all potential functions f for F so that F = ∇f. (If F is not conservative, enter NOT CONSERVATIVE. Use C as an arbitrary constant.)
f(x, y, z) =
Determine if the given vector field F is conservative or not. F = (-5e^y, (-5x + 6z + 8)e^y, 6e^y)
Conservative: conservative
If F is conservative, find all potential functions f for F so that F = ∇f. (If F is not conservative, enter NOT CONSERVATIVE. Use C as an arbitrary constant.)
f(x, y, z) =