A point is moving along the graph of x cubed y squared equals 1600. When the point is at ​(4​,5​), its​ x-coordinate is changing at the rate of negative 3 units per minute.

Question

How fast is the​ y-coordinate changing at that​ moment?

Answer 1

x^3y^2 = 1600

Differentiate implicitly using the product rule:

3x^2(dx/dt)y^2 + x^3(2y)(dy/dt) = 0

3(16)(-3)(25) + (64)(10)(dy/dt) = 0

-3600 + 640(dy/dt) = 0

dy/dt = 3600 / 640 = 5.625