Yeah. The paper says: The derivative of f at c is written f'(c). The derivative of f, written f', is the function c -> f'(c). So the derivative (f') is the res

Yeah. The paper says: The derivative of f at c is written f'(c). The derivative of f, written f', is the function c -> f'(c). So the derivative (f') is the result of substituting c for x in f1. For example, if f1 = (x -> x + c) then we would have f' = (c -> c + c) = (c -> 2c).