If y = e^log sin^-1x + e^log cos^-1x, 0 < x < 1, then

$y = e^{\log \sin^{-1}x} + e^{\log \cos^{-1}x}$

$= \sin^{-1}x + \cos^{-1}x$

as $e^{\log a} = a$

as $\sin^{-1}x + \cos^{-1}x = \frac{\pi}{2}$

$y = \frac{\pi}{2}$

so $\frac{dy}{dx} = 0$