Chapter 6 - Applications of the Derivative - 6.5 Related Rates - 6.5 Exercises - Page 341: 4

$\frac{dy}{dt}=\frac{-3}{14}$

$4x^{3} - 6xy^{2}+3y^{2}= 228$ $12x^{2}\frac{dx}{dt} -12xy\frac{dy}{dt} -6y^{2}\frac{dx}{dt}+6y\frac{dy}{dt}=0$ $(6y-12xy)\frac{dy}{dt}+(12x^{2}-6y^{2})\frac{dx}{dt}=0$ Now substitute x = -3, y = 4, and dx/dt =3 to get $\frac{dy}{dt}=\frac{-3}{14}$