Question

Найти производную функции y=log3(x^3+3)arcsin x

Answer 1

$y=log_3 (x^3+3) arcsin(x)$
$y'=(log_3 (x^3+3))' arcsin(x)+log_3 (x^3+3) arcsin(x)'= \frac{3x^2}{(x^3+3)ln3}=$
$= \frac{3x^2arcsin(x)}{(x^3+3)ln3} + \frac{log_3 (x^3+3) }{ \sqrt{1-x^2} }$