How do you find dy/dx given x=t-1/t and y=2t+1/t?

1 Answer
Nov 8, 2017

dy/dx=-1

Explanation:

dy/dx= color (blue)((dy/dt)/color (brown)(dx/dt)
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color (blue)(dy/dt) and color (brown)(dx/dt) are determined by
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applying the quotient rule.
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color (blue)(dy/dt=?
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dy/dt=((2t+1)'xxt-t'xx (2t+1))/t^2
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dy/dt=(2xxt-1xx (2t+1))/t^2
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dy/dt=(2t-2t-1)/t^2
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color (blue)(dy/dt=-1/t^2
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color (brown)(dx/dt=?
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dx/dt=((t-1)'xxt-t'xx (t-1))/t^2
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dx/dt=(1xxt-1xx (t-1))/t^2
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dx/dt=(t-t+1)/t^2
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color (brown)(dx/dt=1/t^2
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dy/dx=(color (blue)(dy/dt))/(color (brown)(dx/dt))
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dy/dx=(color (blue)(-1/t^2))/(color (brown)(1/t^2))
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dy/dx=-1/t^2xxt^2/1
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therefore dy/dx=-1