Implementing Derivative using linear regression (#137142)

* Initial steps of implementing Derivative using linear regression

* [CI] Auto commit changes from spotless

* Using code generation

* fixup

* [CI] Auto commit changes from spotless

* fixup

* capab

* fixup

* fixup

* try capability rename

* rebase

* fixup

* comments

* resolvetype

* adding docs

* fixup. comments

* fixup

* prototype simpler code from nhat advice

* remove unneeded stuff

* rewrite of deriv

* fixup test

* fixup

* fixcup

* fix docs

* comments

* fix

* fixup

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Co-authored-by: elasticsearchmachine <infra-root+elasticsearchmachine@elastic.co>

Author: pabloem

docs/reference/query-languages/esql/_snippets/functions/description/deriv.md

@@ -15,3 +15,4 @@
 * [`STDDEV_OVER_TIME`](../../functions-operators/time-series-aggregation-functions.md#esql-stddev_over_time) {applies_to}`stack: preview 9.3` {applies_to}`serverless: preview`
 * [`VARIANCE_OVER_TIME`](../../functions-operators/time-series-aggregation-functions.md#esql-variance_over_time) {applies_to}`stack: preview 9.3` {applies_to}`serverless: preview`
 * [`SUM_OVER_TIME`](../../functions-operators/time-series-aggregation-functions.md#esql-sum_over_time) {applies_to}`stack: preview 9.2` {applies_to}`serverless: preview`
+* [`DERIV`](../../functions-operators/time-series-aggregation-functions.md#esql-deriv) {applies_to}`stack: preview 9.3` {applies_to}`serverless: preview`

docs/reference/query-languages/esql/_snippets/functions/examples/deriv.md

@@ -63,3 +63,6 @@ supports the following time series aggregation functions:
 
 :::{include} ../_snippets/functions/layout/sum_over_time.md
 :::
+
+:::{include} ../_snippets/functions/layout/deriv.md
+:::