Use implicit differentiation to find dy/dx. $\ln x y-y^{3}=9$
A) $\frac{x}{y\left(3 y^{3}-1\right)}$
B) $\frac{y\left(3 y^{3}-1\right)}{x}$
C) $\frac{y}{x\left(3 y^{3}-1\right)}$
D) $\frac{x\left(3 y^{3}-1\right)}{y}$

Question

Quizplus · Accepted Answer

Implicit differentiation of $\ln(xy) - y^3 = 9$ gives $\frac{1}{xy}(y + x\frac{dy}{dx}) - 3y^2\frac{dy}{dx} = 0$. Solving for $\frac{dy}{dx}$ yields $\frac{dy}{dx} = \frac{y}{x(3y^3 - 1)}$.

Use Implicit Differentiation to Find Dy/dx ln⁡xy−y3=9\ln x y-y^{3}=9lnxy−y3=9 A) xy(3y3−1)\frac{x}{y\left(3 y^{3}-1\right)}y(3y3−1)x​

Use Implicit Differentiation to Find Dy/dx $\ln x y-y^{3}=9$ A) $\frac{x}{y\left(3 y^{3}-1\right)}$