A function p(x) is said to be a polynomial if it is of the form p(x) = aɖxª + ad−1xd-1 + +α1 x + ao for some real constants a; and for some non-negative integer d > 0. Prove, by using the Principle of Mathematical Induction, that if f(x) = ex², then for every positive integer n, there exists a polynomial p(x) such that f(n) (x) -- the n-th derivative of f -- is equal to ex² · Pn(x). .