Peak–end rule end. The effects of the duration of an experience upon retrospective evaluation are extremely slight. Fredrickson and Kahneman labeled this phenomenon "duration neglect". The peak–end rule is applicable only when an experience has definite beginning and end periods. A 1993 study titled "When More Pain Is Preferred to Less: Adding a Better End" by Kahneman, Fredrickson, Charles Schreiber, and Donald Redelmeier provided groundbreaking evidence for the peak–end rule. Participants were subjected to two different versions of a single unpleasant experience. The first trial had subjects submerge a hand in 14 °C water for 60 seconds. The second trial had subjects
Chain rule for short, The derivative function is therefore: Another way of computing this derivative is to view the composite function as the composite of and "h". Applying the chain rule to this situation gives: This is the same as what was computed above. This should be expected because . Sometimes it is necessary to differentiate an arbitrarily long composition of the form formula_23. In this case, define where formula_25 and formula_26 when formula_27. Then the chain rule takes the form or, in the Lagrange notation, The chain rule can be used to derive some well-known differentiation rules. For example, the quotient