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

1 Answer
Mia
Nov 8, 2017

#dy/dx=-1#

Explanation:

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

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