Question

Помогите найти производные функции

Answer 1

$y :' : (x) =( (1 + sqrt[3]{x} ) ^{2} ) :' = \ = 2(1 + sqrt[3]{x} ) times frac{1}{3} {x}^{ frac{1}{3} - 1 } = \ = frac{2}{3} ( frac{1}{ { sqrt[3]{ {x}^{2} } } } + frac{1}{ sqrt[3]{x} } )$
$y:'(x) = ( frac{3}{ sqrt[3]{ x} } - frac{2}{ sqrt{x} }) :' = \ = 3 cdot ( - frac{1}{3} {x}^{ - frac{1}{3} - 1} ) - \ - 2 cdot( - frac{1}{2} {x}^{ - frac{1}{2} - 1} ) = \ = - {x}^{ - frac{4}{3} } + {x}^{ - frac{3}{2} } = frac{1}{ x sqrt{ {x} } } - frac{1}{x sqrt[3]{x} }$
$y:'(x ) = (x + ctgx):' = \ = 1 - ( {ctg}^{2} x + 1) = - {ctg}^{2} x$