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Implicit Differentiation

AP Calculus AB· difficulty 3/5

For x2+xy+y2=7x^2 + xy + y^2 = 7, dy/dx=dy/dx =

  • A

    2x+yx+2y\dfrac{2x + y}{x + 2y}

  • B

    −2x+yx+2y-\dfrac{2x + y}{x + 2y}

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  • C

    −2x2y\dfrac{-2x}{2y}

  • D

    −xy-\dfrac{x}{y}

Explanation

2x+y+xy′+2yy′=0⇒y′(x+2y)=−(2x+y)⇒y′=−(2x+y)/(x+2y)2x + y + x y' + 2 y y' = 0 \Rightarrow y'(x + 2y) = -(2x + y) \Rightarrow y' = -(2x+y)/(x+2y).

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