Question

помогите решить производную
$sqrt[3]{arccos(sin(x))}$

Answer 1

$frac{d}{dx}[arccos(sin(x))^{ frac{1}{3}}]$
$frac{1}{3} arccos(sin(x))^{ frac{1}{3} -1} frac{d}{dx}[arccos(sin(x))]$
$frac{1}{3} arccos(sin(x))^{ frac{1}{3} + frac{-1}{3} frac{3}{3} } frac{d}{dx} [arccos (sin(x))]$
$frac{1}{3} arccos(sin(x))^{ frac{1}{3} + frac{-1*3}{3} } frac{d}{dx} [arccos(sin(x))]$
$frac{arccos(sin(x))^{- frac{2}{3}} }{3} (- frac{1}{ sqrt{1-sin^2(x)}} frac{d}{dx} [sin(x)] }$
$- frac{arccos(sin(x))^{- frac{2}{3}} }{3 sqrt{1-sin^2(x)} } cos(x)$
$- frac{cos(x)arccos(sin(x))^{- frac{2}{3}}}{3 sqrt{1-sin^2(x)} }$
$- frac{cos(x) frac{1}{arccos(sin(x))^{- frac{2}{3}}} }{3 sqrt{1-sin^2(x)} }$
$- frac{cos(x)}{3arccos(sin(x))^ frac{2}{3} sqrt{1-sin^2(x)} }$