---
title: derivative() function
description: >
  `derivative()` computes the rate of change per unit of time between subsequent
  non-null records.
menu:
  flux_v0_ref:
    name: derivative
    parent: universe
    identifier: universe/derivative
weight: 101
flux/v0/tags: [transformations]
introduced: 0.7.0
---

<!------------------------------------------------------------------------------

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`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
```

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

## 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)

```

{{< expand-wrapper >}}
{{% expand "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   |

{{% /expand %}}
{{< /expand-wrapper >}}

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

```js
import "sampledata"

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

```

{{< expand-wrapper >}}
{{% expand "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   |

{{% /expand %}}
{{< /expand-wrapper >}}