Question

Решите алгебра , 11 класс​

Answer 1

1

$f'(x) = \frac{( \sqrt{x}) '{e}^{ x} - ( {e}^{x})' \sqrt{x} }{ {e}^{2x} } = \\ = \frac{ \frac{1}{2} {x}^{ - \frac{1}{2} } {e}^{x} - {e}^{x} \sqrt{x} }{ {e}^{2x} } = \frac{ {e}^{x}( \frac{1}{2 \sqrt{x} } - \sqrt{x} ) }{e ^{2x} } = \\ = \frac{1}{ {e}^{x} } ( \frac{1}{2 \sqrt{x} } - \sqrt{x} )$

2

$f'(x) = \frac{1}{ ln(9) \times x} \\$

3

$f'(x) = ln(6) \times {6}^{3x} \times (3x)' =3 ln(6) \times {6}^{3x} \\$

4

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