#### To determine

**To state:**

Whether the given statement,"The derivative of a rational number is a rational number" is true or false.

#### Answer

The given statement is true.

#### Explanation

Rational function is ratio of polynomial functions:

fx=pxqx

By using quotient rule, ddxuv=vdudx-udvdxv2

f'x=qxddxpx-pxddxq(x)qx2

As the difference, product, and division of a polynomial function is always polynomial, the derivative of rational function is always a ratio of polynomials.

Hence, derivative of a rational function is a rational function.

Therefore, the statement is true.

**Final statement:**

The given statement is true.