References: The power rule from geometry

Source material

Source curriculum (structural mirror, cited as further study):
• 3Blue1Brown, Essence of Calculus, Chapter 3: "Power Rule through geometry"
  Creator: Grant Sanderson
  Lesson page: https://www.3blue1brown.com/lessons/derivatives-power-rule
  Series index: https://www.3blue1brown.com/?topic=calculus
  License: copyright Grant Sanderson; videos published on his site and YouTube
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Watch this next

• Power Rule through geometry (3Blue1Brown) by Grant Sanderson. The video this lesson mirrors. Watching the square grow two strips and the cube grow three slabs, with the tiny corner pieces shrinking away, is the clearest way to see why the power rule’s n and t^(n-1) are what they are. Sanderson also extends the same picture to 1/x and √x. About thirteen minutes.

Going deeper

• Essence of Calculus (full series) by 3Blue1Brown. The series this track follows. The previous chapter defined the derivative as a limit; the next (Trig Derivatives through geometry) finds the derivatives of sine and cosine by the same nudge-and-look method, using the geometry of a point moving around a circle.

• Khan Academy: Calculus for a slower, exercise-driven treatment of the power rule and basic differentiation rules, with practice problems and immediate feedback.

Adjacent topics

Where this sits in the track.

• The derivative as a rate (previous lesson). That lesson computed d/dt(t^2) and d/dt(t^3) by expanding binomials and taking a limit. This lesson explains the pattern in those answers (the power rule) with a picture, so the binomial grind is never needed again.

• More derivative rules (next lessons). The same geometric, nudge-and-look reasoning gives the derivatives of the trig functions, the product rule (for a product of two functions), and the chain rule (for a function inside a function). Each is a consequence of how a quantity grows when you nudge its input, not a fact to memorize.