The derivative of $xyz$ with respect to $x$ is $yz$, the derivative of $-4y^2z^2$ with respect to $x$ is $0$, and the derivative of $\cos(xy)$ with respect to $x$ is $-y\sin(xy)$. So, we get:
$$yz - 0 - y\sin(xy) = \frac{\partial F}{\partial x}$$
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