What is this story called? It is not There Will Be Soft Rain by Ray Bradbury, but another short story about a fully automatic house that takes a man out of bed, shaves him, gives him breakfast, puts him in a car that drives him to work where his co-workers discover he has been dead for hours.
This is likely the short-story "Yukitodoita seikatsu" by japanese science fiction writer Shinichi Hoshi (1926-97). (Possible title translation: well-kept life)
This is made more likely by the OP's nordic name, as the story was printed in the Norwegian SciFi anthology "Vestenfor Måne" in 1972. Here, the title was translated as "automatisk eksistens" (automatic existence). Norwegian internet users will be able to access the full-text here.
The short-story was also adapted for TV in 2007.
The following summary was written in 2003 by Sayuri Matsushima:
in ‘Yukitodoita seikatsu’, a typical morning for a man living in the future is described. Technology has become so advanced that the man does not need to lift a finger from the moment he wakes up to the moment he arrives at work. The robotic hand wakes him up, shaves him, showers him, gets his breakfast, and even turns on the TV while he is eating. He is placed in the travelling pod and automatically conveyed to his office. It is only when he finally arrives at work that someone notices that he has been dead since the previous night. The situation is novel and interesting, and the surprise ending conveys irony in the fact that people have become so reliant on technology that they can get dressed and arrive at work as a corpse!
For the Norwegian 1972 anthology, the author gave the following introduction to the story:
I have lived in Tokyo all my life. The old Tokyo before the war, the burnt ruins of Tokyo after the war and the modern, rebuilt Tokyo. All three phases of this city I have experienced. How will the cities of the future be? How will life be in those cities? My experiences gave me a hint and this eventually grew into the short-story included in this anthology