Question

Дифференциал функции
$y=arcsin\sqrt{1-2x^2}$

Answer 1

$y=arcsin\sqrt{1-2x^2}\\\\y'=\frac{1}{\sqrt{1-(1-2x^2)}}\cdot (\sqrt{1-2x^2})'=\frac{1}{\sqrt{2x^2}}\cdot \frac{1}{2\sqrt{1-2x^2}}\cdot (1-2x^2)'=\\\\=\frac{1}{|x|\sqrt2}\cdot \frac{1}{2\sqrt{1-2x^2}}\cdot (-4x)=-\frac{\sqrt2\cdot x}{|x|\cdot \sqrt{1-2x^2}}$