d/dx F = F' is indeed a concise way to denote that d (\x.F) = (\x.F), where \x.F is the lambda calculus notation of a function that takes x to F.

The /dx part indicates that the following expression should be considered functions of x.

The equation can also be rewritten as d F = F' dx, reflecting that the change in function value is proportional to both the derivate and change in x.