Chapter 3: Derivatives - Section 3.8 - Related Rates - Exercises 3.8 - Page 161: 6

$\dfrac{dx}{dt} = 55$

Given: $\dfrac{dy}{dt} = 5$ and $x=y^3-y$ Thus, on differentiating $x$ with respect to time, we get and $\dfrac{dx}{dt} = \dfrac{3y^2dy}{dt}-\dfrac{dy}{dt}$ Now, when $y=2$; then$ \dfrac{dx}{dt} = 3\times (4)\times5-5$ Thus, the answer is: $\dfrac{dx}{dt} = 55$