Предмет: Математика, автор: goodfeeling33

15 баллов за подробный ответ дам

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Автор ответа: Miroslava227

Ответ:

$f(x) = \frac{ ln(x) }{ {x}^{2} } \\$

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

$f'(1) = \frac{1 - 2 ln(1) }{1} = \frac{1}{1} = 1 \\$

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