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Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. xy=2 (a) Find `dy/dt` ,given `x=2` and `dx/dt =11` (b) Find `dx/dt` , given `x=1` and `dy/dt=-7` If someone can explain the steps so I understand these types of problems it would mean a lot.   Thanks

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Lix Lemjay eNotes educator | Certified Educator

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The given equation is:

`xy=2`

Take the derivative with respect to t on both sides of the equation.

`d/dt(xy)=d/dt(2)`

Note that the derivative of constant is zero. So right side becomes:

`d/dt(xy)=0`

For the right side, apply the power rule which is`(u*v)'=v*u' + u*v'`.

`ydx/dt+xdy/dt=0`

Now that derivative of the equation with respect to x is known,...

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