I find it best to switch everything exponents when taking derivatives.
F(x) = 7/x
Same as..
F(x) = 7x^-1
Take derivative..
F'(x) = -7x^-2
Plug in x = 1
F'(1) = -7(1)^-2
F'(1) = -7
The first letter can be any of 26.
The second letter can be any of the remaining 25.
The third letter can be any of the remaining 24.
26*25*24 = 15,600 passwords are possible