Question

Помогите найти производные функции

Answer 1

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