Answer
$y=x$
Work Step by Step
$y=x^{sinx}$
$lny=lnx^{sinx}$
$lny=(sinx)(lnx)$
$\frac{dy}{y}=((cosx)(lnx)+\frac{sinx}{x})dx$
$\frac{dy}{dx}=((cosx)(lnx)+\frac{sinx}{x})x^{sinx}$
at $(\frac{\pi}{2},\frac{\pi}{2}),$
$\frac{dy}{dx}=M=(cos(\frac{\pi}{2})ln(\frac{\pi}{2})+\frac{2sin(\frac{\pi}{2})}{\pi})\frac{\pi}{2}^{sin(\frac{\pi}{2})}$
$=(\frac{2}{\pi})(\frac{\pi}{2})$
$=1$
Equation of Tangent:
$y-\frac{\pi}{2}=1(x-\frac{\pi}{2})$
$y=x$
