Calculate $\frac{\partial z}{\partial x}$ and $\frac{\partial z}{\partial y}$ at the points (1, 85, 3) and (1, 85, -3), where z is defined implicitly by the equation $z^4 + z^2x^2 - y - 5 = 0$.
(Give exact answers. Use symbolic notation and fractions where needed.)
$\frac{\partial z}{\partial x}|_{(1,85,3)} = $
$\frac{\partial z}{\partial y}|_{(1,85,3)} = $
$\frac{\partial z}{\partial x}|_{(1,85,-3)} = $
$\frac{\partial z}{\partial y}|_{(1,85,-3)} = $
