Question

Дифференциал функции
$y=arcsinsqrt{1-2x^2}$

Answer 1

$y=arcsinsqrt{1-2x^2}\\y'=frac{1}{sqrt{1-(1-2x^2)}}cdot (sqrt{1-2x^2})'=frac{1}{sqrt{2x^2}}cdot frac{1}{2sqrt{1-2x^2}}cdot (1-2x^2)'=\\=frac{1}{|x|sqrt2}cdot frac{1}{2sqrt{1-2x^2}}cdot (-4x)=-frac{sqrt2cdot x}{|x|cdot sqrt{1-2x^2}}$