How that if the vector field F = Pi + Qj + Rk is conservative and P, Q, R have continuous first-order partial derivatives, then the following is true.
∂P/∂y = ∂Q/∂x = ∂P/∂z = ∂R/∂x = ∂Q/∂z = ∂R/∂y.
Since F is conservative, there exists a function f such that F = ∇f, that is, P, Q, and R are defined as follows. (Enter your answers in the form fx, fy, fz.)