a particle moves along the elliptical path given by 4x^2 + y^2=4 in such a way that it is at the point ( √3/2,1), its x-coordinate is increasing at the a rate of 5 units per seconds. How fast is the y-coordinate changing at that instant?

use implicit derivatives.

8x dx/dt + 2y dy/dt = 0
8(√3/2)(5) + 2*1 dy/dt = 0
...