Comments by "David Terr" (@dcterr1) on "Why are the formulas for the sphere so weird? (major upgrade of Archimedes' greatest discoveries)" video.

  1. I stopped the video at 17:57. I first learned the proof of the derivative formulas for the circumference of a circle and the surface area of a sphere when I learned how to solve rate of change problems. Just make the radius of the circle or the sphere, as the case may be, a variable and note that the rate of change of the area of the circle or the volume of the sphere, as the case may be, is just the circumference of the circle or the surface area of the sphere, respectively, times the rate of change of the radius. Voila!
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