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Implicit Differentiation

AP Calculus AB· difficulty 3/5

For y3=x2+7y^3 = x^2 + 7, dy/dxdy/dx at the point (1,2)(1, 2) is

  • A

    23\tfrac{2}{3}

  • B

    13\tfrac{1}{3}

  • C

    16\tfrac{1}{6}

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  • D

    22

Explanation

3y2y′=2x⇒y′=2x/(3y2)3y^2 y' = 2x \Rightarrow y' = 2x/(3y^2). At (1,2)(1, 2): 2/(3⋅4)=1/62/(3 \cdot 4) = 1/6.

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