To derange someone is to make her go crazy or completely confuse her. Going without sleep for an entire week can derange a person.
It's more common to see the adjective deranged — or insane — than the verb derange, but you can use it to describe what happens when someone or something drives a person batty. Too many head injuries can derange a football player's short term memory, and a teasing cat just out of reach might derange a tied-up dog in a yard. The Old French root of derange is desrengier, "throw into disorder," which combines des, "do the opposite of" and rengier, "put into line."