DIFFERENTIATION OF DETERMINANTS

() g(x) Let A(x)= $2(x) 82(x)| where fi(x), f2(x), 8ı (x) and 32(x) are functions of x. f(x) g(x) f(x) g(x) Then, A'(x) = $2(x) 82(x)/" $2(x) g(x) f(x) g(x) f(x) g(x) Also, A'(x) = $(x) 82(x)["\2(x) gź(x) + X X +

f1 f (x)

a Thus, to differentiate a determinant, we differentiate one row (or column) at a time, keeping others unchanged.