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

Expert Answers

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The given equation is:


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


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


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


Now that derivative of the equation with respect to x is known, use this and the given equation to solve the two problems.

(A) `x=2` and `dx/dt=11` ,   `dy/dt=?`

Before substituting the given values to the derivative, solve for y first.

To do so, plug-in x=2  to:




Now that value of y is known, plug-in x=2, y=1 and `dx/dt=11` to:






Hence, when `x=2` and `dx/dt=11` , `dy/dt=-11/2` .

(B) `x=1` and `dy/dt=-7` ,  `dx/dt= ?`

Do the same steps as above. Plug-in x=1 to the given equation to solve for y.




Then, substitute x=1, y=2 and `dy/dt=-7` to:






Hence, when `x=1` and `dy/dt=-7` , `dx/dt=7/2` .

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