**Derivative of a polynomial**

In derivation, we can use derivation rules, i.e. the derivative does not have to be determined through the limit value of the difference quotient.

The derivation rules are as follows. In these, D means a derivative.

The exponent is brought in front as a coefficient and the exponent is reduced by one.

The derivative of the variable alone is 1.

The coefficient of the term can be taken in front of the derivative. The derivative of a first degree term becomes only the coefficient of the term.

The derivative of all constants is 0.

In addition, the polynomial function is derived term by term.

**Example 1**

The exponent is brought in front as a coefficient and the exponent is reduced by one.

The exponent is brought in front as a coefficient and the exponent is reduced by one.

The derivative of *x* alone is *1*, so only a coefficient remains from the first degree term.

The derivative of all constants is *0*.

**Example 2**

Differentiate the functions *f*, *g *and *h*

Differentiate each function term by term.

**Turn on the subtitles if needed**