Mathematics

Problem

The path of a roller-coaster loop is modeled by

x\tan y-y^{2}=0

, where

x

and

y

are measured in meters. Determine

\dfrac{dy}{dx}

when

y=\dfrac{\pi}{4}

. a)

-\dfrac{4}{\pi(\pi-4)}

\dfrac{8}{\pi(\pi-4)}

-\dfrac{8}{\pi(\pi-4)}

-\dfrac{8}{\pi(\pi+4)}