Question

Производная показательной и логарифмической функции. Помогите решить!!!

Answer 1

Ответ:

1.

$( {e}^{x} + 1)' = e {}^{x}$

2.

$= {e}^{x} + 2x$

3.

$= {e}^{2x + 1} \times (2x + 1) '+ 6 {x}^{2} = \\ = 2 {e}^{2x + 1} + 6 {x}^{2}$

4.

$= {e}^{1 - x} \times(1 - x)' - 3 {x}^{ - 4} = \\ = - {e}^{1 - x} - \frac{3}{ {x}^{4} }$

5.

$= \frac{2}{ x} + ln(3) \times {3}^{x}$

6.

$= \frac{3}{x} - ln(2) \times {2}^{x}$

7.

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

8.

$= - 9 {x}^{ - 4} - \frac{1}{ ln(3) \times x } = - \frac{9}{ {x}^{4} } - \frac{1}{x ln(3) }$

9.

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

10.

$= \cos(x) + 2x$

11.

$= - \sin(x) + {e}^{x}$

12.

$= \cos(x) - ln(2) \times {2}^{x}$

13.

$= \cos(2x - 1) \times (2x - 1) '= 2 \cos(2x - 1)$

14.

$= - \sin(x + 2) \times (x + 2) '= - \sin(x + 2)$

15.

$= \cos(3 - x) \times (3 - x)' = - \cos(3 - x)$

16.

$= - \sin( {x}^{3} ) \times ( {x}^{3})' = - 3 {x}^{2} \sin( {x}^{3} )$