Question: Suppose P and Q are polynomials and is a positive integer. Use mathematical induction to prove that the nth derivative of the rational function f(x)

Suppose P and Q are polynomials and is a positive integer. Use mathematical induction to prove that the nth derivative of the rational function f(x) = P(x) / Q(x) can be written as a rational function with denominator [Q(x)] n+1. In other words, there is a polynomial An such that f (n)(x) = An (x) / [Q(x)] n + 1.

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