Let A and B be two n×n matrices with real entries. Define the function f : R → R by f(x) = det(A + Bx)

(i) Show that f⁽³⁾(x) = 3! det B.
(ii) Show that in general f⁽ⁿ⁾(x) = n! det B.

f⁽ⁿ⁾(x) is the nth derivative of f(x).