Mathematics

Problem

Consider the function

y=(\sin x)^{x}

defined for

x\in(0,\pi)

. (i) Establish that

y

is differentiable on the open interval

(0,\pi)

. (ii) Determine

\dfrac{dy}{dx}

in its simplest form. (iii) Hence, calculate the value of

\dfrac{dy}{dx}

x=\dfrac{\pi}{3}