題組內容

II. (50 points) Fill in the following blanks.

4. Assume that $z$ and $w$ are differentiable functions of $x$ and $y$, satisfying the equations $xw^3 + yz^2 + z^3 = -1$ and $zw^3 - xz^3 + y^2w = 1$. Then, at $(x, y, z, w) = (1, -1, -1, 1)$, $\frac{\partial z}{\partial x} =$ __(4)__.