Chapter 3.4, Problem 3ES

Both $x$ and $y$ denote functions of $t$ that are related by the given equation. Use this equation and the given derivative information to find the specified derivative.

Equation: $4x^2+9y^2=1$ .

(a) Given that $dx/dt=3$ , find $dy/dt$ when $\left(x,y\right)=\left(\frac{1}{2\sqrt{2}},\frac{1}{3\sqrt{2}}\right)$ .

(b) Given that $dy/dt=8$ find $dx/dt$ when $\left(x,y\right)=\left(\frac{1}{3},-\frac{\sqrt{5}}{9}\right)$ .