Derivative of a Rational Polynomial Function

The derivative of a rational polynomial function also is a rational polynomial function. Using the quotient rule, you obtain the derivative of a rational polynomial function from the derivatives of the numerator and denominator polynomials. According to the quotient rule, the following equation yields the first derivative of the rational polynomial function .

You can derive the second derivative of a rational polynomial function from the first derivative, as shown by the following equation.

You continue to derive rational polynomial function derivatives such that you derive the j derivative of a rational polynomial function from the (j - 1) derivative.