Lesson 4.2Math~50 min

Derivative shortcuts

A handful of rules that let you find slopes without zooming at all.

Module 4 · 0/7 done

Draw the slope of every point

The derivative isn’t just one number — at every $x$ the curve has a slope, so the slopes themselves form a new function, $f'(x)$ . Trace it yourself: drag the point along the top curve, and each slope you visit is plotted underneath.

Fig 4.3Top: a function and its tangent. Bottom: the slope at each point you’ve visited. Try x² — its slopes trace out a straight line, 2x.