A Point Is Moving Along The Graph Of X Cubed Y Squared Equals 1600 When The

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

Solution

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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