The divergence of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by ∇ · F = ∂P/∂x + ∂Q/∂y + ∂R/∂z.
For F(x, y, z) = x^4i - x^3z^2j + 4xy^2zk, we have P(x, y, z) = x^4, Q(x, y, z) = -x^3z^2, and R(x, y, z) = 4xy^2z. So, ∇ · F = 4x^3 - 2x^3z^2
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