Chapter 6 - Applications of the Derivative - 6.5 Related Rates - 6.5 Exercises - Page 341: 3

$\frac{dy}{dt}=\frac{9}{7}$

$2xy - 5x +3y^{3}= -51$ $2x\frac{dy}{dt} + 2y\frac{dx}{dt}-5\frac{dx}{dt}+9y^{2}\frac{dy}{dt}=0$ $(2x+9y^{2})\frac{dy}{dt}+(2y-5)\frac{dx}{dt}=0$ Now substitute x = 3, y = -2, and dx/dt = -6 to get $(2(3)+9(-2)^{2})\frac{dy}{dt} +[2(-2)-5](-6)=0$ $\frac{dy}{dt}=\frac{9}{7}$