Use implicit differentiation to find dy/dx.
-$x y + x + y = x ^ { 2 } y ^ { 2 }$
A) $\frac { 2 x y ^ { 2 } + y } { 2 x ^ { 2 } y - x }$
B) $\frac { 2 x y ^ { 2 } + y + 1 } { - 2 x ^ { 2 } y - x - 1 }$
C) $\frac { 2 x y ^ { 2 } - y } { 2 x ^ { 2 } y + x }$
D) $\frac { 2 x y ^ { 2 } - y - 1 } { - 2 x ^ { 2 } y + x + 1 }$

Question

Quizplus · Accepted Answer

Differentiating both sides of the equation $x y + x + y = x ^ { 2 } y ^ { 2 }$ with respect to $x$, we get:$$y + x \frac{dy}{dx} + 1 + \frac{dy}{dx} = 2x y^2 + x^2(2y \frac{dy}{dx})$$Rearranging to solve for $\frac{dy}{dx}$, we get:$$\frac{dy}{dx}(x + 1 + 2x^2y) = 2xy^2 - y - 1$$Thus, $\frac{dy}{dx} = \frac{2xy^2 - y - 1}{x + 1 + 2x^2y}$, which simplifies to:$\frac{dy}{dx} = \frac{2xy^2 - y - 1}{-2x^2y + x + 1}$, matching choice D.

Use Implicit Differentiation to Find Dy/dx xy+x+y=x2y2x y + x + y = x ^ { 2 } y ^ { 2 }xy+x+y=x2y2

Use Implicit Differentiation to Find Dy/dx $x y + x + y = x ^ { 2 } y ^ { 2 }$