Question

Проиводные у=(sinx) ^x

Answer 1

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