Mathematics

Problem

Let

x=e^{2t}

and

y=e^{t}+t

. Determine

\dfrac{dy}{dx}

at the value of

t

that satisfies

\sin t=\dfrac{1}{2}

with

0<t<\pi

. a)

\dfrac{e^{\pi/6}+1}{e^{\pi/3}}

\dfrac{e^{\pi/6}+1}{2e^{\pi/3}}

\dfrac{2e^{\pi/3}}{e^{\pi/6}+1}

\dfrac{e^{\pi/6}+1}{2e^{\pi/6}}