y^2 = 2 + xy; at t = 5, y = 3, dy/dt = 6; find dx/dt

Math wiz ya rite 09

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Let x and y be functions of time t that are related by the equation y^2 = 2 +xy. At time t=5, the value of y is 3 and dy/dt =6. Find the value of dx/dt at time =5.

Note: The derivative of y^2 = 2 + xy = y / (2y - x)
 
Re: calc2

Hello, Math wiz ya rite 09!

I explained this at another site . . .


Let x\displaystyle x and y\displaystyle y be functions of time t\displaystyle t
that are related by the equation: y2=2+xy\displaystyle \, y^2 \:=\: 2\, +\,xy
At time t=5:  y=3\displaystyle t\,=\,5:\;y\,=\,3 and dydt=6\displaystyle \frac{dy}{dt}\,=\,6

Find the value of dxdt\displaystyle \frac{dx}{dt} at t=5.\displaystyle t\,=\,5.

When t=5,y=3        32=2+3x        x=73\displaystyle t\,=\,5,\:y\,=\,3\;\;\Rightarrow\;\;3^2\:=\:2\,+\,3x\;\;\Rightarrow\;\;x\,=\,\frac{7}{3}


Differentiate the equation with respect to \(\displaystyle t:\;\;\L 2y\cdot\frac{dy}{dt}\;=\;x\cdot\frac{dy}{dt}\,+\,y\cdot\frac{dx}{dt}\)

And we know: x=73,  y=3,  dydt=6\displaystyle \:x\,=\,\frac{7}{3},\;y\,=\,3,\;\frac{dy}{dt}\,=\,6 .. . . Go fot it!

 
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