Answer
TRUE
Work Step by Step
Differentiate a rational function as:
$f'(x)=(\frac{P(x)}{Q(x)})'=\frac{P'(x)Q(x)-Q'(x)P(x)}{Q^{2}(x)}$
Since the derivative of a polynomial is a polynomial and the sum, difference, or product of two polynomials is a polynomial, we have that $f'(x)$ is still a ratio of two polynomials (a rational function).
Hence, the given statement is true.
