Please prove equation (28). This is from Quantum Field Theory in a Nutshell by Zee

Appendix 3 To do an exponential integral of the form I = if le(\"5V\") we often have to resort to the steepest-descent approximation, which I will now review for your convenience. In the limit of h small, the integral is dominated by the minimum of f(q). Expanding f(q) = f(a) + a f\"(a)(q a)2 + 0[(q a)3] and applying (17) we obtain 1 ' l I = e(l/hma) ( 2m )2 60012) (27) f \"(a) For f (q) a function of many variables 611 . . . , q N and with a minimum at q j = a j, we generalize immediately to 1 N _ l I = e(l/)f(a) ( LIE) )2 (30012) (28) det f \" ((1) Here f\"(a) denotes the N by N matrix with entries [f\"(a)],-j E (32f/3qi8qj)|q:a. In many situations, we do not even need the factor involving the determinant in (28). If you can derive (28) you are well on your way to becoming a quantum eld theorist