Question

ПОМОГИТЕ ПОЖАЛУЙСТА, ДАЮ 100 БАЛЛОВ

Answer 1

Ответ:

22.1.

1.

$f'(x) = ln(3) \times {3}^{ {x}^{2} - 7x } \times ( {x}^{2} - 7x) '= \\ = ln(7) \times {3}^{ {x}^{2} - 7x } \times (2x - 7)$

2.

$f'(x) = ln(2) \times {2}^{x + 3 {x}^{2} } \times (x + 3 {x}^{2} )' = \\ = ln(2) \times {2}^{x + 3 {x}^{2} } \times (1 + 6x)$

3.

$f'(x) = ln(0.8) \times {0.8}^{1 - {x}^{3} } \times (1 - {x}^{3} ) '= \\ = ln( {8}^{ - 1} ) \times {0.8}^{1 - {x}^{3} } \times ( - 3 {x}^{2} ) = \\ = - ln(8) \times 0.8 {}^{1 - {x}^{3} } \times ( - 3 {x}^{2} ) = \\ = 3 {x}^{2} ln(8) \times {0.8}^{1 - {x}^{3} }$

4.

$f'(x) = ln( \frac{1}{7} ) \times {( \frac{1}{7} )}^{4 - x} \times ( - 1) = \\ = - ln(7) \times {( \frac{1}{7} )}^{4 - x} \times ( - 1) = \\ = ln(7) \times {7}^{x - 4}$

22.2

1.

$f'(x) = 1 - \frac{5}{x} \\ f'(1) = 1 - 5 = - 4$

2.

$f'(x) = \frac{1}{8} \times \frac{2}{2x} = \frac{1}{8x} \\ f'(3) = \frac{1}{24}$

22.3

1.

$f'(x) = \frac{1}{(2 + x) \times ln(0.5) } \\ f'(1) = \frac{1}{3 \times ln(0.5) } = - \frac{1}{3 ln(2) }$

2.

$f'(x) = \frac{1}{(5 + x) \times ln(3) } \\ f'(4) = \frac{1}{9 ln(3) }$

3.

$f'(x) = ln(0.2) \times {0.2}^{x - 3} = \\ = - ln(5) \times {0.2}^{x - 3} = \\ = - ln(5) \times {5}^{3 - x} \\ f'(4) = - ln(5) \times {5}^{ - 1} = - \frac{ ln(5) }{5}$

4.

$f'(x) = ln(2.5) \times {2.5}^{x - 1} \\ f'(2) = ln(2.5) \times 2.5 = \\ = 2.5 ln(2.5)$