Discrete Derivative in SQL

Select a.Time as StartTime
     , b.time as EndTime
     , b.time-a.time as TimeChange
     , b.value-a.value as ValueChange
FROM YourTable a 
Left outer Join YourTable b ON b.time>a.time
Left outer Join YourTable c ON c.time<b.time AND c.time > a.time
Where c.time is null
Order By a.time

you could use a SQL window function, below is an example based on BIGQUERY syntax.

SELECT 
  LAG(time, 1) OVER (BY time) AS start_time,
  time AS end_time, 
  (value - LAG(value, 1) OVER (BY time))/value AS Change
from data

Select a.Time as StartTime, b.time as EndTime, b.time-a.time as TimeChange, b.value-a.value as ValueChange
FROM YourTable a, YourTable b
WHERE b.time = (Select MIN(c.time) FROM YourTable c WHERE c.time>a.time)