Find $\frac { d y } { d x }$ , where $x y ^ { 3 } - 3 x ^ { 2 } = 7 y$ .
A) $y ^ { 3 } - 6 x - 7$
B) $\frac { 6 x - y ^ { 3 } } { 3 x y ^ { 2 } - 7 }$
C) $y ^ { 3 } - 6 x$
D) $\frac { 6 x ^ { 2 } } { y ^ { 3 } }$

Question

Quizplus · Accepted Answer

To find $\frac { d y } { d x }$, we differentiate both sides of the equation $x y ^ { 3 } - 3 x ^ { 2 } = 7 y$ with respect to $x$, using the product rule and chain rule where necessary. Differentiating $x y ^ { 3 }$ gives $y^3 + 3xy^2 \frac{dy}{dx}$, and differentiating $-3x^2$ gives $-6x$. On the right side, differentiating $7y$ gives $7\frac{dy}{dx}$. Setting these equal gives $y^3 + 3xy^2 \frac{dy}{dx} - 6x = 7\frac{dy}{dx}$. Solving for $\frac{dy}{dx}$ gives $\frac{dy}{dx} = \frac{6x - y^3}{3xy^2 - 7}$, which matches choice B.

Find dydx\frac { d y } { d x }dxdy​ , Where

Find $\frac { d y } { d x }$ , Where