Question

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)

Answer 1

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.