Where $F$ is the equation of a force and $\phi$ is a distance function with $$ \phi(r)=38\left[e^{-8\left(r-1.25\right)}-2e^{-4\left(r-1.25\right)}\right]+38.5 $$
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Is your problem defined in cartesian or cylindrical coordinates? Depending on this you will apply the gradient to $\phi$ in such coordinates.
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$\begingroup$ The problem just sais it is a model for the energy (kcal/mol) of a system of two particles as a function of the distance... I think that the problem is not properly enunciated... $\endgroup$ Dec 30, 2019 at 13:37
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$\begingroup$ Well, since the energy only depends on the distances of two particles, I'd assumed spherical coordinates, you just need to derive with respect to r. So the force is F = 304*(e^(10 - 8*r) - e^(5 - 4*r))*e_r where e_r is the radial unit vector. Review the calculations. $\endgroup$– V.J.Dec 30, 2019 at 14:20