Question

Решите производную сложной функции

Answer 1

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