Monkey Rule 4
The next two Monkey Rules have to do with the derivatives of specific functions. First we start with the exponential function ex which is plotted below. As usual, a point A has been plotted on the graph, and the tangent line, g, to the function at A has been created. Use your usual code
(x(A),slope(g))
to track the slope of the tangent line as A moves, and get a look at the graph of the derivative of ex.If you're a tad confused, that's normal. It is true that the point B you created is exactly equal to point A. But what does that mean? Well, if you stop and think, it can only mean one thing: that the derivative of ex is itself! And that's our next monkey rule:
Monkey Rule 4: The derivative of ex is ex (itself!).
Quick check: If f(x)=e^x, what is f'(0)?