tex]...

kissofevg @kissofevg

July 2022 1 7 Report

знайти похідну функції f(x)=x^2+1/x-2
[tex]f(x)=\frac{x^{2}+1 }{x-2}[/tex]

Answers & Comments

Miroslava227

Ответ:

$f(x) = \frac{ {x}^{2} + 1}{x - 2} \\$

$f'(x) = \frac{( {x}^{2} + 1)'(x - 2) - (x - 2)'( {x}^{2} + 1)}{ {(x - 2)}^{2} } = \\ = \frac{2x(x - 2) - ( {x}^{2} + 1)}{{( {x}^{} - 2) {}^{2} } } = \frac{2 {x}^{2} - 4x - {x}^{2} - 1 }{ {(x - 2)}^{2} } = \\ = \frac{ {x}^{2} - 4x - 1}{ {(x - 2)}^{2} }$

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