Question

Найти производную функции

Answer 1

Ответ:

а

$y = ln(x) + {x}^{3}$

$y '= \frac{1}{x} + 3 {x}^{2}$

б

$y = \frac{ {x}^{2} + 3}{2 - x}$

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

в

$y = {tg}^{2} x$

$y '= 2tgx \times (tgx) '= \frac{2tgx}{ \cos {}^{2} (x) }$