response.ShouldBeValid();
var projectsPerMonth = response.Aggs.DateHistogram("projects_started_per_month");
projectsPerMonth.Should().NotBeNull();
projectsPerMonth.Buckets.Should().NotBeNull();
projectsPerMonth.Buckets.Count.Should().BeGreaterThan(0);

foreach (var item in projectsPerMonth.Buckets.Skip(1))
{
    var commitsDerivative = item.Derivative("commits_derivative");
    commitsDerivative.Should().NotBeNull();
    commitsDerivative.Value.Should().NotBe(null);
}

s => s
.Size(0)
.Aggregations(a => a
    .DateHistogram("projects_started_per_month", dh => dh
        .Field(p => p.StartedOn)
        .Interval(DateInterval.Month)
        .Aggregations(aa => aa
            .Sum("commits", sm => sm
                .Field(p => p.NumberOfCommits)
            )
            .Derivative("commits_derivative", d => d
                .BucketsPath("commits")
            )
        )
    )
)

new SearchRequest<Project>
{
    Size = 0,
    Aggregations = new DateHistogramAggregation("projects_started_per_month")
    {
        Field = "startedOn",
        Interval = DateInterval.Month,
        Aggregations =
            new SumAggregation("commits", "numberOfCommits") &&
            new DerivativeAggregation("commits_derivative", "commits")
    }
}

{
  "size": 0,
  "aggs": {
    "projects_started_per_month": {
      "date_histogram": {
        "field": "startedOn",
        "interval": "month"
      },
      "aggs": {
        "commits": {
          "sum": {
            "field": "numberOfCommits"
          }
        },
        "commits_derivative": {
          "derivative": {
            "buckets_path": "commits"
          }
        }
      }
    }
  }
}