I need to give a short presentation on introducing a class of engineering students to the concept and definition of the derivative. I'm to assume that the students are currently at the appropriate place in first quarter calculus to support the delivery. In particular, they would have been introduced to the limit, be able to compute limits for many interesting examples, had a treatment of continuity and understand what a removable discontinuity is.
So the general question here is, just take a time-tested standard treatment from a textbook, or try to do something fancier or outside the box? More particularly, introduce it as a textbook would (derive the definition and then compute examples), or jump right into computation using the definition of derivative, and then "motivate" or derive this definition?