If $\ln 7 x y = 6 , \text { find } d y / d x$
A) $\frac { d y } { d x } = - \frac { y } { x }$
B) $\frac { d y } { d x } = - \frac { 7 y } { x }$
C) $\frac { d y } { d x } = - \frac { y } { 7 x }$
D) $\frac { d y } { d x } = - \frac { 7 y } { 6 x }$
E) $\frac { d y } { d x } = - \frac { 6 y } { 7 x }$

Question

Quizplus · Accepted Answer

Differentiating both sides of the equation $\ln(7xy) = 6$ with respect to $x$ using the chain rule and the product rule gives $\frac{1}{7xy} \cdot (7y + 7x\frac{dy}{dx}) = 0$. Simplifying this equation leads to $\frac{dy}{dx} = -\frac{y}{x}$.

If ln⁡7xy=6, find dy/dx\ln 7 x y = 6 , \text { find } d y / d xln7xy=6, find dy/dx

If $\ln 7 x y = 6 , \text { find } d y / d x$