Chapter 3: Derivatives - Section 3.8 - Related Rates - Exercises 3.8 - Page 161: 5

$\dfrac{dy}{dt} = -6$

Given: $\dfrac{dx}{dt} = 3$ and $y=x^2$ Thus, on differentiating $y$ with respect to time, we get $\dfrac{dy}{dt} = \dfrac{2xdx}{dt}$ or, $\dfrac{dy}{dt} = (2x)(3)=6x$ Now, when x=-1; then $ \dfrac{dy}{dt} = (6) (-1)$ Thus, the answer is $\dfrac{dy}{dt} = -6$