Question

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

Answer 1

`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`