If xy^2=12 and dy/dt=6, find dx/dt when y=2

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SUMMARY

The discussion focuses on solving the equation xy²=12 to find dx/dt when given dy/dt=6 and y=2. The correct approach involves using the chain rule to differentiate the equation, leading to the expression (1)(y²) + x(y)(dy/dt) = 0. By substituting y=2 into the equation, x can be determined as x=12/y², which simplifies to x=3. Consequently, dx/dt can be calculated using the derived values.

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If xy^2=12 and dy/dt=6, find dx/dt when y=2

The way i thought to do this would be
(1)(y^2)+x(y)(dy/dt)=0 but i don't know x so this isn't working, what am i doing wrong
 
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You just multiply the derivative of x with respect to y by 6(chain rule). You can find x as a function of y by solving for it so x=12/y^2.
 

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