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We want the derivative of three x squared plus one, all to the fourth power.

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It is a function inside a function: the outside is u to the fourth, and the inside is u equals three x squared plus one.

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The chain rule: differentiate the outside, keep the inside unchanged, then multiply by the derivative of the inside.

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The outside derivative is four u cubed, which is four times three x squared plus one, cubed.

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The inside derivative is six x.

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Multiply them: twenty four x, times three x squared plus one, cubed.

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To recap: name the inside, differentiate the outside, and never forget to multiply by the derivative of the inside.