---
title: derivative() function
description: derivative() computes the rate of change per unit of time between subsequent non-null records.
url: https://docs.influxdata.com/flux/v0/stdlib/universe/derivative/
estimated_tokens: 2542
product: Flux
version: v0
---

# derivative() function

-   Flux 0.7.0+
-   View InfluxDB support

`derivative()` computes the rate of change per unit of time between subsequent non-null records.

The function assumes rows are ordered by the `_time`.

#### Output tables

The output table schema will be the same as the input table. For each input table with `n` rows, `derivative()` outputs a table with `n - 1` rows.

##### Function type signature

```js
(
    <-tables: stream[A],
    ?columns: [string],
    ?initialZero: bool,
    ?nonNegative: bool,
    ?timeColumn: string,
    ?unit: duration,
) => stream[B] where A: Record, B: Record
```

For more information, see [Function type signatures](/flux/v0/function-type-signatures/).

## Parameters

### unit

Time duration used to calculate the derivative. Default is `1s`.

### nonNegative

Disallow negative derivative values. Default is `false`.

When `true`, if a value is less than the previous value, the function assumes the previous value should have been a zero.

### columns

List of columns to operate on. Default is `["_value"]`.

### timeColumn

Column containing time values to use in the calculation. Default is `_time`.

### initialZero

Use zero (0) as the initial value in the derivative calculation when the subsequent value is less than the previous value and `nonNegative` is `true`. Default is `false`.

### tables

Input data. Default is piped-forward data (`<-`).

## Examples

-   [Calculate the non-negative rate of change per second](#calculate-the-non-negative-rate-of-change-per-second)
-   [Calculate the rate of change per second with null values](#calculate-the-rate-of-change-per-second-with-null-values)

### Calculate the non-negative rate of change per second

```js
import "sampledata"

sampledata.int()
    |> derivative(nonNegative: true)
```

[](#view-example-input-and-output)

View example input and output

#### Input data

| _time | _value | *tag |
| --- | --- | --- |
| 2021-01-01T00:00:00Z | -2 | t1 |
| 2021-01-01T00:00:10Z | 10 | t1 |
| 2021-01-01T00:00:20Z | 7 | t1 |
| 2021-01-01T00:00:30Z | 17 | t1 |
| 2021-01-01T00:00:40Z | 15 | t1 |
| 2021-01-01T00:00:50Z | 4 | t1 |

| _time | _value | *tag |
| --- | --- | --- |
| 2021-01-01T00:00:00Z | 19 | t2 |
| 2021-01-01T00:00:10Z | 4 | t2 |
| 2021-01-01T00:00:20Z | -3 | t2 |
| 2021-01-01T00:00:30Z | 19 | t2 |
| 2021-01-01T00:00:40Z | 13 | t2 |
| 2021-01-01T00:00:50Z | 1 | t2 |

#### Output data

| _time | _value | *tag |
| --- | --- | --- |
| 2021-01-01T00:00:10Z | 1.2 | t1 |
| 2021-01-01T00:00:20Z |  | t1 |
| 2021-01-01T00:00:30Z | 1 | t1 |
| 2021-01-01T00:00:40Z |  | t1 |
| 2021-01-01T00:00:50Z |  | t1 |

| _time | _value | *tag |
| --- | --- | --- |
| 2021-01-01T00:00:10Z |  | t2 |
| 2021-01-01T00:00:20Z |  | t2 |
| 2021-01-01T00:00:30Z | 2.2 | t2 |
| 2021-01-01T00:00:40Z |  | t2 |
| 2021-01-01T00:00:50Z |  | t2 |

### Calculate the rate of change per second with null values

```js
import "sampledata"

sampledata.int(includeNull: true)
    |> derivative()
```

[](#view-example-input-and-output)

View example input and output

#### Input data

| _time | _value | *tag |
| --- | --- | --- |
| 2021-01-01T00:00:00Z | -2 | t1 |
| 2021-01-01T00:00:10Z |  | t1 |
| 2021-01-01T00:00:20Z | 7 | t1 |
| 2021-01-01T00:00:30Z |  | t1 |
| 2021-01-01T00:00:40Z |  | t1 |
| 2021-01-01T00:00:50Z | 4 | t1 |

| _time | _value | *tag |
| --- | --- | --- |
| 2021-01-01T00:00:00Z |  | t2 |
| 2021-01-01T00:00:10Z | 4 | t2 |
| 2021-01-01T00:00:20Z | -3 | t2 |
| 2021-01-01T00:00:30Z | 19 | t2 |
| 2021-01-01T00:00:40Z |  | t2 |
| 2021-01-01T00:00:50Z | 1 | t2 |

#### Output data

| _time | _value | *tag |
| --- | --- | --- |
| 2021-01-01T00:00:10Z |  | t1 |
| 2021-01-01T00:00:20Z | 0.45 | t1 |
| 2021-01-01T00:00:30Z |  | t1 |
| 2021-01-01T00:00:40Z |  | t1 |
| 2021-01-01T00:00:50Z | -0.1 | t1 |

| _time | _value | *tag |
| --- | --- | --- |
| 2021-01-01T00:00:10Z |  | t2 |
| 2021-01-01T00:00:20Z | -0.7 | t2 |
| 2021-01-01T00:00:30Z | 2.2 | t2 |
| 2021-01-01T00:00:40Z |  | t2 |
| 2021-01-01T00:00:50Z | -0.9 | t2 |

#### Related

-   [Calculate the rate of change](/influxdb/v2/query-data/flux/rate/)
-   [InfluxQL – DERIVATIVE()](/influxdb/v1/query_language/functions/#derivative)

[transformations](/flux/v0/tags/transformations/)