Продифференцировать функции. Created by nuriknematov123321. algebra-ru

Продифференцировать функции...

nuriknematov123321 @nuriknematov123321

August 2021 1 9 Report

Продифференцировать функции

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Miroslava227

Ответ:

$y' = U'V+ V'U = \\ = \frac{1}{6} {( \frac{x - 7}{x + 7}) }^{ - \frac{5}{6} } \times \frac{x + 7 - (x - 7)}{ {(x + 7)}^{2} } \times arcsin(2x + 3) + \frac{1}{ \sqrt{1 - {(2x + 3)}^{2} } } \times 2 \times \sqrt[6]{ \frac{x - 7}{x + 7} } = \\ = \frac{1}{6} \sqrt[6]{ \frac{ {(x + 7)}^{5} }{ {(x - 7)}^{5} } } \times \frac{14}{ {(x + 7)}^{2} } arcsin(2x + 3) + \frac{2}{ \sqrt{1 - 4 {x}^{2} - 12x - 9} } \times \sqrt[6]{ \frac{x - 7}{x + 7} } = \\ = \frac{7arcsin(2x + 3)}{3 \sqrt[6]{ {(x - 7)}^{5} {(x + 7)}^{7} } } + \sqrt[6]{ \frac{x - 7}{x + 7} } \times \frac{2}{ \sqrt{ - 4 {x}^{2} - 12x - 8} }$

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