One Rule for Every Exponent, Until the x Moves Upstairs

You'll learnthe two moves of the power rule, where they come from, how to rewrite roots and fractions so the rule can see them, and the one shape it says nothing about.

Taking a limit by hand for every function would be unbearable. Here is the first shortcut: shrink a chord on x³ and watch 3x² fall out, then see how far the same two moves reach. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · REWRITE FIRST, THEN ONE RULE · x IN THE BASE, NEVER IN THE EXPONENT · v2

d/dx[ xⁿ ] = n xⁿ⁻¹ · every real n

Before you start

What you're looking at

The curve x³ with a point marked at x = 1, and a chord from that point that is about to shrink.

The question

Is there a shortcut for the slope of any power of x, and where exactly does it stop working?

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