Question

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:

Answer 1

S = dF/dr

So, what's F?

If you mean dU/dr, then that would be

Am/r^(m+1) - Bn/r^(n+1)

Answer 2

F is dU/dr, but your answer is not right :(