Figuring out the rest of the Monkey Rules
We're going to discover the remaining Monkey Rules by playing with Geogebra, and seeing if we can "backwards-engineer" them. If you take an algebra-based calculus course, you'd spend a lot of time "forward-engineering" these by doing numerous differential quotient calculations. We are not going to do that.
To get started, I've plotted the first five power functions from our atomic functions list from Chapter 1. Use the following snippets of code one at a time to start making some educated guesses about the derivatives of these power functions.
derivative(f_0) derivative(f_1) derivative(f_2)
derivative(f_3) derivative(f_4)After you've spent some time conjecturing on the pattern, move forward to see what it is.