I don't know what F is, but
dU/dr = Am/r^(m+1) - Bn/r^(n+1)
So, plug in r0 and you have
dU/dr(r0) = Am/r0^(m+1) - Bn/r0^(n+1)
The energy-separation curve for two atoms, a distance, r, apart is: U(r)=−A/r^m+B/r^n
Derive and expression for the stiffness of the bond at the equilibrium spacing, in terms of A, B, m, n, and r0.
S=dF/dr at r=r0:
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