Question

Найдите производную первого порядка
$y=(arccosx) ^ sqrt{cosx}$

Answer 1

$y = (arc cos x)^{sqrt {cos x}} \ y'=(ln(arc cos x)^{sqrt {cos x}})'*(arc cos x)^{sqrt {cos x}}=(sqrt {cos x}*ln(arc cos x))'*(arc cos x)^{sqrt {cos x}}=$$(- frac{sinx}{2 sqrt{cosx} } *ln(arccosx)+sqrt{cosx}* frac{1}{arccosx}*(- frac{1}{ sqrt{1-x^2} }))*arccosx^{sqrt {cos x}}=$$- frac{sinx*(arccosx)^{sqrt {cos x}}*ln(arccosx)}{2 sqrt{cosx}}-sqrt{ frac{cosx}{1-x^2} }*(arccosx)^{sqrt {cos x}-1}$