$\text { Use implicit differentiation to find } \frac { d y } { d x } \text {. }$ $7 x ^ { 2 } + 8 \ln x y = 14$
A) $- \frac { y \left( 7 x ^ { 2 } + 4 \right) } { 4 x }$
B) $\frac { 7 x ^ { 2 } y } { 4 }$
C) $- \frac { 7 x ^ { 2 } } { 4 y }$
D) $- \frac { y \left( 7 x ^ { 2 } - 8 \right) } { 4 x }$
E) $- \frac { 7 x ^ { 2 } y } { 4 }$

Question

Quizplus · Accepted Answer

To find $\frac{dy}{dx}$, differentiate both sides of the equation $7x^2 + 8\ln(xy) = 14$ with respect to $x$, using the product rule and chain rule as necessary. Differentiating $7x^2$ gives $14x$, and differentiating $8\ln(xy)$ gives $8\left(\frac{1}{xy}\right)(y + xy')$ by the product rule and chain rule. Setting the derivative equal to 0 and solving for $y'$ yields $- \frac { y \left( 7 x ^ { 2 } + 4 \right) } { 4 x }$.

Use implicit differentiation to find dydx. \text { Use implicit differentiation to find } \frac { d y } { d x } \text {. } Use implicit differentiation to find dxdy​.

$\text { Use implicit differentiation to find } \frac { d y } { d x } \text {. }$