Find dy/dx by implicit differentiation.
-$x^{3}+3 x^{2} y+y^{3}=8$
A) $-\frac{x^{2}+2 x y}{x^{2}+y^{2}}$
B) $\frac{x^{2}+3 x y}{x^{2}+y^{2}}$
C) $-\frac{x^{2}+3 x y}{x^{2}+y^{2}}$
D) $\frac{x^{2}+2 x y}{x^{2}+y^{2}}$

Question

Quizplus · Accepted Answer

To find dy/dx by implicit differentiation, we differentiate both sides of the equation with respect to x, treating y as a function of x.Differentiating the left side, we get:3x^2 + 6xy + y^2 dy/dxDifferentiating the right side, we get:0Setting the two derivatives equal to each other, we get:3x^2 + 6xy + y^2 dy/dx = 0Solving for dy/dx, we get:dy/dx = - (3x^2 + 6xy) / y^2Simplifying, we get:dy/dx = - (x^2 + 2xy) / y^2Therefore, the correct answer is A) - (x^2 + 2xy) / y^2.

Find Dy/dx by Implicit Differentiation x3+3x2y+y3=8x^{3}+3 x^{2} y+y^{3}=8x3+3x2y+y3=8 A) −x2+2xyx2+y2-\frac{x^{2}+2 x y}{x^{2}+y^{2}}−x2+y2x2+2xy​

Find Dy/dx by Implicit Differentiation $x^{3}+3 x^{2} y+y^{3}=8$ A) $-\frac{x^{2}+2 x y}{x^{2}+y^{2}}$