Question

Найти производную функции:

Answer 1

$\displaystyle\bf\\y=\sqrt[3]{1-4x^{2} } =\Big(1-4x^{2} \Big)^{\dfrac{1}{3} } \\\\\\y'=\frac{1}{3} \cdot\Big(1-4x^{2} \Big)^{\frac{1}{3}-1 }\cdot(1-4x^{2} )'=\frac{1}{3} \cdot\Big(1-4x^{2} \Big)^{-\frac{2}{3} }\cdot(-8x)=\\\\\\=-\frac{8x}{3} \cdot\frac{1}{\sqrt[3]{(1-4x^{2} )^{2} } } =-\frac{8x}{3\sqrt[3]{(1-4x^{2} )^{2} } }$