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