This paper explores how textbooks address two central concepts in differential calculus, derivative at a point and derivative function, make the transition from one concept to the other, and establish connections between them. We analyzed how the three most widely used calculus textbooks present these two aspects of the derivative, focusing on visual means and word use in the books. In contrast to their thorough discussion on the limit process for the derivative at a point, the books make a quick transition to the derivative function by "letting a point 'a' vary" and changing "f'(a) to f'(x)." Then, they graph f'(x) using several values of the derivative at a point. In addition, the books often use the term "derivative" without specifying which of the two concepts is meant, and are inconsistent in the use of letters, so that it is unclear whether a letter (a or x[subscript 1]) denotes an arbitrary but fixed number or a variable. [For the complete proceedings, see ED584829.]