Vector Analysis 2.4. DIFFERENTIATION RULES 32. Gravitational and electromagnetic forces are acting on a charged particle in space. Let F = F(x, y, z) be the magnitude of the net force, in Newtons, which acts on the particle at the position (x, y, z) meters. Suppose that, at (x, y, z) = (1, 3, 2), the partial derivatives of F, in N/m, are: Fₓ = 4.5, Fᵧ = 10, and Fz = -2. If the position of the particle, in meters, at time t seconds, is given by: p(t) = (t², t³ + 2t + 1), what is the rate of change of the magnitude of the net force on the particle, with respect to time, at time t = 1?

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