Find dy/dx by implicit differentiation.
-$x^{3}+y^{3}=5$
A) $\frac{y^{2}}{x^{2}}$
B) $\frac{x^{2}}{y^{2}}$
C) $-\frac{x^{2}}{y^{2}}$
D) $-\frac{y^{2}}{x^{2}}$

Name: Find dy/dx by implicit differentiation. -$x^{3}+y^{3}=5$ A) $\frac{y^{2}}{x^{2}}$ B) $\frac{x^{2}}{y^{2}}$ C) $-\frac{x^{2}}{y^{2}}$ D) $-\frac{y^{2}}{x^{2}}$
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Question

Quizplus · Accepted Answer

Differentiating both sides with respect to x gives $3x^2 + 3y^2 \frac{dy}{dx} = 0$. Solving for $\frac{dy}{dx}$ gives $\frac{dy}{dx} = -\frac{x^2}{y^2}$.

Find Dy/dx by Implicit Differentiation x3+y3=5x^{3}+y^{3}=5x3+y3=5 A) y2x2\frac{y^{2}}{x^{2}}x2y2​ B) x2y2\frac{x^{2}}{y^{2}}y2x2​ C) −x2y2-\frac{x^{2}}{y^{2}}−y2x2​ D) −y2x2-\frac{y^{2}}{x^{2}}−x2y2​

Find Dy/dx by Implicit Differentiation $x^{3}+y^{3}=5$ A) $\frac{y^{2}}{x^{2}}$ B) $\frac{x^{2}}{y^{2}}$ C) $-\frac{x^{2}}{y^{2}}$ D) $-\frac{y^{2}}{x^{2}}$