Question

Знайти похідну функції

Answer 1

Ответ:

1.

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

2.

$y' = ( {x}^{2} )'ctgx + (ctgx)' \times {x}^{2} = \\ = 2xctgx - \frac{ {x}^{2} }{ \sin {}^{2} (x) }$

3.

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