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Implicit Differentiation

AP Calculus AB· difficulty 4/5

For the curve x2+xy+y2=7x^2 + xy + y^2 = 7, dydx\dfrac{dy}{dx} at the point (1,2)(1, 2) equals

  • A

    −1-1

  • B

    −23-\frac{2}{3}

  • C

    −45-\frac{4}{5}

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  • D

    45\frac{4}{5}

Explanation

Differentiate: 2x+y+x y′+2y y′=02x + y + x\,y' + 2y\,y' = 0 → y′=−(2x+y)/(x+2y)y' = -(2x+y)/(x+2y). At (1,2): y′=−(2+2)/(1+4)=−4/5y' = -(2+2)/(1+4) = -4/5.

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