AP Calculus ABmediummcq1 pt

If y = x³ + 2xy + y² = 3, find dy/dx using implicit differentiation:

A.(-3x²)/(2x + 2y)

B.(3x² + 2y)/(2x + 2y)

C.(-3x² - 2y)/(2x + 2y)

D.(3x²)/(2x + 2y)

Explanation

Differentiating: 3x² + 2y + 2x(dy/dx) + 2y(dy/dx) = 0. Solving: (2x + 2y)dy/dx = -3x² - 2y, so dy/dx = (-3x² - 2y)/(2x + 2y).

C(-3x² - 2y)/(2x + 2y)

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