Question

Equation: 4x^2+9y^2=1
Given that dy/dt=8, find dx/dt when (x,y)=(1/3 , -((sqrt5)/9)

Answer 1

full differential

8x dx/dt + 18 y dy/dt=0

8x dx/dt+ 18 y 8=0
8x dx/dt + 144 y=0

dx/dt=a
8/3 a + 144 (-((sqrt5)/9)=0

solve for a(aka dx/dt)