Assume that x and y are both differentiable functions of t. Find $\frac { d x } { d t }$ when $x = 11$ and $\frac { d y } { d t } = - 8$ for the equation $x y = 132$.
A) $\frac { d x } { d t } = - 1056$
B) $\frac { d x } { d t } = 88$
C) $\frac { d x } { d t } = - \frac { 22 } { 3 }$
D) $\frac { d x } { d t } = \frac { 22 } { 3 }$
E) $\frac { d x } { d t } = - 88$

Question

Quizplus · Accepted Answer

Using the product rule, we have:$$\frac{d}{dt}(xy) = x\frac{dy}{dt} + y\frac{dx}{dt}$$Substituting the given values, we get:$$11(-8) + 132\frac{dx}{dt} = 0$$Solving for $\frac{dx}{dt}$, we get:$$\frac{dx}{dt} = \frac{88}{132} = \frac{22}{3}$$

Assume That X and Y Are Both Differentiable Functions of T