## Thomas' Calculus 13th Edition

$\dfrac{dx}{dt} = 3$
Given: $\dfrac{dy}{dt}=-2$ and $2x+3y=12$ Thus,on differentiating $y$ with respect to time, we get $\dfrac{d(2x+3y)}{dt}$ = $\frac{d (12)}{dt}$ or, $2\dfrac{dx}{dt} + 3\dfrac{dy}{dt}=0$ or, $2\dfrac{dx}{dt} = (-3)(-2)$ Thus, the answer is :$\dfrac{dx}{dt} = 3$