## Calculus (3rd Edition)

$$\phi (x,y,z) = \sin (x y z)+K$$
Given $$\mathbf{F}=\langle y z \cos (x y z), x z \cos (x y z), x y \cos (x y z)\rangle$$ We need to find $\phi(x,y,z)$ such that $$\frac{\partial \phi }{\partial x} = y z \cos (x y z),\ \ \ \ \frac{\partial \phi }{\partial y} = x z \cos (x y z),\ \ \ \ \frac{\partial \phi }{\partial z} =xy \cos (x y z)$$ Then \begin{align*} \phi(x,y,z)&= \sin (x y z)+C_1\\ \phi(x,y,z)&= \sin (x y z)+C_1\\ \phi(x,y,z)&= \sin (x y z)+C_1 \end{align*} Hence, we can choose $$\phi(x,y,z)= \sin (x y z)+K$$