Question

Самостоятельная работа по теме «Производные некоторых элементарных функций»
Вариант 3
1.Найти производную функции:
1) e^(4х+3)-х5; 2) cos (6x +4); 3) ln x• sin 2x;
4) sin ( 3 - x/6); 5) 〖1+ e〗^3x/cos⁡x ; 6) 5^x + ln ( 6x+3);
7) ln ( x2 + 4x); 8) log 6 x.

Answer 1

Ответ:

1.

$y= {e}^{4x + 3} - {x}^{5}$

$y '= {e}^{4x + 3} \times (4x + 3)' - 5 {x}^{4} = \\ = 4 {e}^{4x + 3} - 5 {x}^{4}$

2.

$y = \cos(6x + 4)$

$y' = - \sin(6x + 4) \times ( 6x + 4)' = \\ = - 6 \sin(6x + 4)$

3.

$y = ln(x) \times \sin(2x)$

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

4.

$y = \sin(3 - \frac{x}{6} )$

$y' = \cos(3 - \frac{x}{6} ) \times ( - \frac{1}{6} ) = \\ = - \frac{1}{6} \cos(3 - \frac{x}{6} )$

5.

$y = \frac{(1 + e) {}^{3x} }{ \cos(x) }$

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

6.

$y = {5}^{x} + ln(6x + 3)$

$y' = ln(5) \times {5}^{x} + \frac{1}{6x + 3} \times 6$

7.

$y = ln( {x}^{2} + 4x )$

$y' = \frac{1}{ {x}^{2} + 4x } \times (2x + 4)$

8.

$y' = log_{6}(x) \\ y = \frac{1}{x ln(6) }$