Question

Найти производную функции y=x^(sin(x))
$y = {x}^{ sin(x) }$

Answer 1

$y=x^{sin(x)}$
$ln(y)=ln(x^{sin(x)})$
$ln(y)=sin(x)*ln(x)$
$frac{y'}{y} =cos(x)*ln(x)+ frac{sin(x)}{x}$
$y' =y(cos(x)*ln(x)+ frac{sin(x)}{x} )$
$y' =x^{sin(x)}*(cos(x)*ln(x)+ frac{sin(x)}{x} )$