Derivatives Chain Rule

Derive the chain rule by thinking about hiking up a mountain: we can measure your posistion along a map as $x(t)$ and also the height of a mountain $h(x)$. But what is your actual change in height over time; how steep is your hike?

Try to guess the form: what is it proportional to? To the steepeness of the slope? To your speed walking?

“Derive” the chain rule by looking at the slope of a nearby secant line.