Repeated Differentiation and Polynomial Degree

Repeated Differentiation and Polynomial Degree

If $$P(x)$$ is a polynomial of degree $$n$$, then:

$$P^{(n)}(x)=n!a_n$$

where $$a_n$$ is the leading coefficient.

Also:

$$P^{(n+1)}(x)=0$$

Usage

- Used to identify polynomial degree and leading coefficients through higher derivatives.