Question

y= x*arcsin sqrt1-4x

Answer 1

$y=xcdot arcsinsqrt{1-4x}\\y'=arcsinsqrt{1-4x}+xcdot frac{1}{sqrt{1-(1-4x)}}cdot frac{1}{2sqrt{1-4x}}cdot (-4)=\\=arcsinsqrt{1-4x}-frac{2x}{2sqrt{x}cdot sqrt{1-4x}}=arcsinsqrt{1-4x}-sqrt{frac{x}{1-4x}}$