Chapter 6 - Applications of the Derivative - 6.5 Related Rates - 6.5 Exercises - Page 341: 6

$\frac{dy}{dt}=\frac{555}{71}$

$\frac{y^{3}-4x^{2}}{x^{3}+2y}=\frac{44}{31}$ $31y^{3}-124x^{2}=44x^{3}+88y$ $93y^{2} \frac{dy}{dt}-248x\frac{dx}{dt}=132x^2\frac{dx}{dt}+88\frac{dy}{dt}$ $(248x+132x^{2})\frac{dx}{dt}=(93y^{2}-88)\frac{dy}{dt}$ Now substitute x =-3, y = -2, and dx/dt =5 to get $\frac{dy}{dt}=\frac{555}{71}$