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The power rule says the derivative of x to the n is n times x to the n minus one.

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Bring the power down in front, then lower the power by one.

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Differentiate three x to the fourth, minus two x squared, plus seven x, one term at a time.

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Three times four x cubed, minus two times two x, plus seven, because the derivative of x is one.

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So the derivative is twelve x cubed minus four x plus seven.

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The derivative gives the slope of the tangent line.

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At x equals one, twelve minus four plus seven is fifteen.

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To recap: apply the power rule to each term, keep the constant multipliers, and plug in a value of x to get a tangent slope.