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let xy=2 and let dy/dt=2 find dx/dt when x=2 related rates

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You need to differentiate the given function with respect to t, using the product rule such that:

`(dx)/(dt)*y + x*(dy)/(dt) = 0`

You may substitute `2/x`  for `y`  such that:

`(dx)/(dt)*(2/x) + x*(dy)/(dt) = 0`

Since the problem provides the values `(dy)/(dt) = 2`  and `x = 2` , you may substitute the values in equation above such that:

`(dx)/(dt)*(2/2) + 2*2 = 0 => (dx)/(dt) + 4 = 0 => (dx)/(dt) = -4`

Hence, evaluating `(dx)/(dt)`  under the given conditions yields `(dx)/(dt) = -4` .

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