Suppose 4x^2+9y^2=36, where x and y are functions of t. If dy/dt=1/3, find dx/dt when x=2 and y=2/3*sqrt (5)

The derivative of the function in terms of t is,

2 (4x) (dx / dt) + 2 (9y) (dy / dt) = 0

Substituting the known values from the given above gives,

2 (4) (2) (dx / dt) + 2 (9) (2/3) (sqrt of 5) (1 / 3) = 0

Solving the equation gives a value of dx/dt equal to - 0.559.