Question

Найти производную показательной функции:

Answer 1

6

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

х = 0

$y' = 3 {e}^{0} + ln(5) \times {5}^{0} = 3 + ln(5)$

7

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

8

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

9

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

10

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

$y'' = {e}^{ {x}^{2} + 3x } \times (2x + 3) \times (2x + 3) + 2 {e}^{ {x}^{2} + 3x} = \\ = {e}^{ {x}^{2} + 3x} ( {(2x + 3)}^{2} + 2) = {e}^{ {x}^{2} + 3x} (4 {x}^{2} + 24x + 9 + 2) = \\ = {e}^{ {x}^{2} + 3x } (4 {x}^{2} + 24x + 11)$