I'm beginning to think that Walkelin de Ferrers-400 isn't from the Ferrers family at all, and that his wife Goda, isn't from the Toeni/Tosny family. The Wikipedia article that Janet has linked to above, doesn't actually cite any sources for the section titled Living, where his parents, her parents, and their children are mentioned.
K.S.B Keats-Rohan, Domesday Descendants: A Prosopography of Persons Occurring in English Documents 1066-1166, vol. 2 Pipe Rolls to Cartae Baronum, (Woodbridge, Suffolk : Boydell Press, 2002). doesn't mention either Walkelin or Goda in the articles about their supposed fathers.
As well as providing for Derby School, they appear to have something to do with Darley Abbey but I can only see snippet views of some of the texts related to both of these. See The Cartulary of Darley Abbey, vol 1 and The Victoria History of the County of Derby, vol, 2.
The charter to grant house and land to Derby School is available in Educational charters and documents 598 to 1909 by Arthur Francis Leach. The charter has original latin and English translations side by side, starting on bottom of pp. 110 & 111, and then over the page to top of pp. 112 & 113.
From what I can see in the snippet views, there is a son Peter of Derby, who might just be the son of Goda, and also a son Robert, who might be a son of both or just of Walkelin.
The Derbyshire Record Office catalogue, has a number of charters where a Robert son of Walkelin is one of the witnesses. See here as an example. It seems likely this is the same man and I think if he was from the Ferrers family his name would be mentioned, not just Robert son of Walkelin, particularly as he is witnessing a grant by William de Ferrers, Earl of Derby.