## p.. y (Polynomial Derivative)

The first derivative of a given polynomial y

• got from differentiating the individual terms of the series

NB: the derivative of the first term (a constant) is omitted from the result.

Polynomial y can be provided either in the form of coefficients (in ascending powers) or in (m;r) format (multiplier and roots). See: Roots (p.) .

Examples:

•  Series 1 x x² x³ x⁴ 1st derivative 1 2x 3x² 4x³

```   p.. 1 1 1 1 1
1 2 3 4```
•  Series 1 2x 3x² 4x³ 5x⁴ 1st derivative 2 6x 12x² 20x³

```   p.. 1 2 3 4 5
2 6 12 20```

### Common uses

Work with finite approximations of infinite series.

## x p.. y (Polynomial Integral)

The integral of a given polynomial y

• got from integrating the individual terms of the series

The x-argument is the constant term that needs to be provided.

The y-argument can be provided either in the form of coefficients (in ascending powers) or in (m;r) format (multiplier and roots). See: Polynomial (p.) .

Examples: (invert the examples in monadic p.. above)

•  Series 1 2x 3x² 4x³ Integral n x x² x³ x⁴

```   99 p.. 1 2 3 4
99 1 1 1 1```
•  Series 2 6x 12x² 20x³ Integral n 2x 3x² 4x³ 5x⁴

```   1 p.. 2 6 12 20
1 2 3 4 5```

### Common uses

Work with finite approximations of infinite series.