Question

Проиводные у=(sinx) ^x

Answer 1

$y=(\sin x)^x = e^{\ln (\sin x)^x} = e^{x \ln \sin x} \\ y'= e^{x \ln \sin x} \cdot (x \ln \sin x)' = (\sin x)^x \cdot ( \ln \sin x+\frac{x \cos x}{\sin x} ) =\\ = (\sin x)^x \cdot ( \ln \sin x+x ctgx )$