Let #xy=2# and let #(dy)/(dt)=5#. What is #(dx)/(dt)# where #x=3#?

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Answer 1 · 2016-11-05T17:05:07

#(dx)/(dt)=-2/3#

#(dx)/(dt)=(dx)/(dy)xx(dy)/(dt)#

we need to find #(dy)/(dx)#

#xy=2=>y=2/x=2x^-1#

#(dy)/(dx)=-2x^-2=-2/x^2#

#((dy)/(dx))_(x=3)=-2/9#

#:.(dx)/(dy)=-9/2#

#:.(dx)/(dt)=-9/2xx3=-6/9=-2/3#