Question

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Answer 1

Ответ:

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

$y '= 2( \frac{1}{ \sqrt[3]{ {x}^{2} } } - \frac{1}{ \sqrt[4]{x} } ) \times ( {x}^{ - \frac{2}{3} } - {x}^{ - \frac{1}{4} } ) '= \\ = 2( \frac{1}{ \sqrt[3]{ {x}^{2} } } - \frac{1}{ \sqrt[4]{x} } ) \times ( - \frac{2}{3} {x}^{ - \frac{5}{3} } + \frac{1}{4} {x}^{ - \frac{5}{4} } ) = \\ = ( \frac{2}{ \sqrt[3]{ {x}^{2} } } - \frac{2}{ \sqrt[4]{x} } ) \times ( - \frac{2}{3 \sqrt[3]{ {x}^{5} } } + \frac{1}{4 \sqrt[4]{ {x}^{5} } } ) = \\ = - \frac{4}{3 {x}^{ \frac{2}{3} + \frac{5}{3} } } + \frac{2}{ {x}^{ \frac{2}{3} + \frac{5}{4} } } + \frac{4}{3 {x}^{ \frac{1}{4} + \frac{5}{3} } } - \frac{2}{ {x}^{ \frac{1}{4} + \frac{5}{4} } } = \\ = - \frac{4}{3 {x}^{2} \sqrt[3]{x} } + \frac{2}{ {x}^{ \frac{23}{12} } } + \frac{4}{3 {x}^{ \frac{2}{3} } } - \frac{2}{ {x}^{ \frac{3}{2} } } = \\ = - \frac{4}{3 {x}^{2} \sqrt[3]{x} } + \frac{2}{x \sqrt[12]{ {x}^{11} } } + \frac{4}{3 \sqrt[3]{ {x}^{2} } } - \frac{2}{x \sqrt{x} }$