Chapter 3 - Section 3.10 - Related Rates - Exercises - Page 187: 4

$\frac{dx}{dt} = 3$

Work Step by Step

Given that $\frac{dy}{dt}$ = -2 and $2x+3y=12$ on differentiating y with respect to time $\frac{d(2x+3y)}{dt}$ = $\frac{d 12}{dt}$ $\frac{d2x}{dt}+\frac{d3y}{dt}$ = $0$ so $2\frac{dx}{dt} + 3\frac{dy}{dt}$ = 0 $2\frac{dx}{dt} = -3 \times (-2)$ Thus, the answer is $\frac{dx}{dt} = 3$

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