Question

Найдите производную




$y = \sqrt[3]{ {x}^{4} \sqrt[6]{x \sqrt[3]{x} } }$

Answer 1

$y' = ( \sqrt[3]{ {x}^{4} \sqrt[6]{x \sqrt[3]{x} } } )' = ( \sqrt[3]{ {x}^{4} \sqrt[6]{ \sqrt[3]{x^4} } } )' = ( \sqrt[3]{ \sqrt[6]{{x}^{24} * \sqrt[3]{x^4} } } )' = \\ \\ = ( \sqrt[3]{ \sqrt[6]{ \sqrt[3]{x^{72} * x^4} } } )' = ( \sqrt[54]{ x^{76} })' = \frac{38}{27} * x^{ \frac{11}{27} } = \frac{38}{27} * \sqrt[27]{x^{11} }$