Y= x*arcsin sqrt1-4x

[latex]y=x\cdot arcsin\sqrt{1-4x}\\\\y'=arcsin\sqrt{1-4x}+x\cdot \frac{1}{\sqrt{1-(1-4x)}}\cdot \frac{1}{2\sqrt{1-4x}}\cdot (-4)=\\\\=arcsin\sqrt{1-4x}-\frac{2x}{2\sqrt{x}\cdot \sqrt{1-4x}}=arcsin\sqrt{1-4x}-\sqrt{\frac{x}{1-4x}}[/latex]