Now let's try calculating another derivative of a more complicated function. Let's try our function [code]g(x)[/code] which [url=https://www.geogebra.org/m/x39ys4d7#material/aayx7rmz]models the height of an incoming missile[/url].[br][br]Even though [code]g(x)[/code] is more complicated, we'll use a shortcut in Geogebra to make this even easier than before. [br][br]I've added a point to the function, and I've also added the tangent line. All you have to do is type the following code into the input bar to have Geogebra calculate the derivative automatically:[br][br][code]derivative(g)[br][/code]

YES Geogebra knows how to calculate derivatives. This is a huge help.[br][br]Before we get too hung up on this revelation, move the blue dot along [code]g(x)[/code], and notice that the breadcrumb trail matches the automatically calculated derivative exactly! [br][br]Just to be clear about what's going on, as you move the blue dot, the slope of the tangent line to [code]g(x)[/code] is being encoded by the black dot, and the black dot is moving along the derivative[code] g'(x)[/code]. I know there's a lot of moving parts, but this is the crux of understanding derivatives, so hang in there.[br][br]In the next activity we're going to see a quick application that will shed more light on the concept of a derivative.