Question

Найдите производную функцию 
$y = 3 \sqrt[3]{ {x}^{2} } + \frac{1} { {x}^{2} } + 3x$

Answer 1

$y = 3 x^{ \frac{2}{3} } + x^{-2} +3x$
$y' = (3 x^{ \frac{2}{3} } + x^{-2} +3x)' = (3 x^{ \frac{2}{3} })' + (x^{-2})' +(3x)' =[tex]=3* \frac{2}{3}* x^{ ( \frac{2}{3}-1)} +(-2)* x^{-2-1}+3*1* x^{1-1} =$$=2* x^{- \frac{1}{3} } -2 x^{-3}+3 x^{0} =$$= \frac{2}{ \sqrt[3]{x} } - \frac{2}{ x^{3} } +3$