Question

Помогите пожалуйста. СРОЧНО. ОЧЕНЬ НУЖНО. Даю 45 баллов ​

Answer 1

Ответ:

1.

$y' = 10 {x}^{4} - 5 \times ln(2) \times {2}^{x} + 4 - \frac{7}{x ln(2) } - 0 = \\ = 10 {x}^{4} - 5 ln(2) \times {2}^{x} + 4 - \frac{7}{x ln(2) }$

2.

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

3.

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