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The chain rule isn't a formula to memorize — it's a rate inside a rate, and the two rates MULTIPLY. Take y = (x²)³. There's an inner function and an outer one: inner: u = x² — at x = 1 its slope is g′ = 2 (u changes twice as fast as x) outer: y = u³ — at u = 1 its slope is f′ = 3 (y changes 3× as fast as u) Stack the two graphs ...
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