The function is given by:
\(F(x, y, z) = 5(x - 2) - 10\arctan(yz)\)
Now, we find the partial derivatives with respect to x, y, and z:
\(\frac{\partial F}{\partial x} = 5\)
\(\frac{\partial F}{\partial y} = -10\frac{z}{1 + y^2z^2}\)
\(\frac{\partial
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