Let $\frac { y } { x } = 12$ If $\frac { d x } { d t } = - \frac { 1 } { 2 },$ then $\frac { d y } { d t }$ is

A)-6
B)-4
C)-2
D)2
E)6

Question

Let $\frac { y } { x } = 12$ If $\frac { d x } { d t } = - \frac { 1 } { 2 },$ then $\frac { d y } { d t }$ is

A)-6
B)-4
C)-2
D)2
E)6

Quizplus · Accepted Answer

Given $\frac{y}{x} = 12$, differentiating both sides with respect to $t$ gives $\frac{d}{dt}(\frac{y}{x}) = \frac{d}{dt}(12)$. Applying the quotient rule, we get $\frac{x\frac{dy}{dt} - y\frac{dx}{dt}}{x^2} = 0$. Substituting $\frac{dx}{dt} = -\frac{1}{2}$ and $\frac{y}{x} = 12$ into the equation, we solve for $\frac{dy}{dt}$ to find it equals -6.

Let yx=12\frac { y } { x } = 12xy​=12 If dxdt=−12,\frac { d x } { d t } = - \frac { 1 } { 2 },dtdx​=−21​,

Let $\frac { y } { x } = 12$ If $\frac { d x } { d t } = - \frac { 1 } { 2 },$