Let and . Determine at the value of that satisfies with…

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

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}}

(b)

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

(c)

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

(d)

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

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