Question

Найти производную функции

Answer 1

$y'=(x^2*arcsin(sqrt{1-x^2}))'=\=(x^2)'*arcsin(sqrt{1-x^2})+x^2*(arcsin(sqrt{1-x^2}))'=\=2x*arcsin(sqrt{1-x^2})+x^2*frac{1}{sqrt{1-(sqrt{1-x^2})^2}}*(sqrt{1-x^2})'=\=2xarcsin(sqrt{1-x^2})-frac{x^2}{sqrt{1-{(sqrt{1-x^2})^2}}}*(-frac{x}{sqrt{1-x^2}})$