помогите пожалуйста найти производную функции. Created by laktina20009. matematika-ru

помогите пожалуйста найти производную функции...

laktina20009 @laktina20009

July 2022 1 6 Report

помогите пожалуйста найти производную функции

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Miroslava227

Ответ:

$y' = 0 + 1 - \frac{1}{2} \times 4 {x}^{3} = 1 - 2 {x}^{3} \\$

$y' = \frac{1}{2} \times \frac{( {x}^{2} )'(x - 1) - (x - 1) '\times {x}^{2} }{ {(x - 1)}^{2} } = \\ = \frac{1}{2} \times \frac{2x(x - 1) - {x}^{2} }{ {(x - 1)}^{2} } = \frac{2 {x}^{2} - 2x - {x}^{2} }{2 {(x - 1)}^{2} } = \\ = \frac{ {x}^{2} - 2x}{2 {(x - 1)}^{2} }$

$y '= \frac{( {x}^{2} )'( {x}^{3} + 8) - ( {x}^{3} + 8) '\times {x}^{2} }{ {( {x}^{3} + 8)}^{2} } = \\ = \frac{2 x({x}^{3} + 8) - 3 {x}^{2} \times {x}^{2} }{ {( {x}^{3} + 8)}^{2} } = \\ = \frac{2 {x}^{4} + 16x - 3 {x}^{4} }{ {( {x}^{3} + 8) }^{2} } = \frac{16x - {x}^{4} }{ {( {x}^{3} + 8)}^{2} }$

$y '= \frac{5( {x}^{2} - 4) - 2x \times 5x}{ {(x {}^{2} - 4)}^{2} } = \\ = \frac{5 {x}^{2} - 20 - 10 {x}^{2} }{ {( {x}^{2} - 4)}^{2} } = - \frac{5 {x}^{2} + 20 }{ {( {x}^{2} - 4) }^{2} }$

$y '= \frac{4 {x}^{3} ( {x}^{3} - 1) - 3 {x}^{2} \times {x}^{4} }{ {( {x}^{3} - 1)}^{2} } = \\ = \frac{4 {x}^{6} - 4 {x}^{3} - 3 {x}^{6} }{ {( {x}^{3} - 1)}^{2} } = \frac{ {x}^{6} - 4 {x}^{3} }{ {( {x}^{3} - 1)}^{2} }$

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