Question

y=³корень (3х+1)²

Найти производную

Answer 1

$\displaystyle y=\sqrt[2]{(3x+1)^2}=(3x+1)^{\frac{2}{3} }\\\\\\y'=\frac{2}{3} (3x+1)^{^{\frac{2}{3}-1} }\,\times(3x+1)'=\frac{2}{3} (3x+1)^{^{-\frac{1}{3}} }\times3=\\\\\\=\frac{2}{(3x+1)^{^{\frac{1}{3}} }} =\frac{2}{\sqrt[3]{3x+1} }$