I recall the first few days of my f

I recall the first few days of my first calculus course where we learned about derivatives of functions. We performed some rather hairy computations using limits to
arrive at the derivatives ofseveral functions. Even though the functions were simple, the work involved in calculating the derivatives was nightmarish.
After several homework assignments, study groups, and an exam, most everyone
in the class was able to do the work. But the tedium of it was nearly unbearable. If
this was the first thing we’d learn in a class named “Calculus I,” then what monstrosity of mathematics awaited us mid-semester in “Calculus II”?
Then the instructor clued us in on a trick. Applying a simple formula made
quick work of calculating derivatives (if you’ve ever taken calculus, you’ll know what