let xy=4 and let dy/dt=1 find dx/dt when x=2

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The variables x and y are related by `xy=4` .

Take the derivative with respect to t.

=> `x*(dy/dt) + y*(dx/dt) = 0` ...(1)

When x = 2, y = 2. Also `dy/dt = 1` . Substituting these values in (1)

`2*1 + 2*(dy/dt) = 0`

=> `dy/dt = -1`

The required value of `dy/dt = -1` .

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