Question

Найдите производную :

1)e^x - sinx

1/x^2 + e^x

e^x -ctgx

2)-5e^2x

-3sin2x

2e^2x - 4e^-2x

Answer 1

Ответ:

1)

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

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

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

2)

$y = - 5 {e}^{2x} \\ y' = - 5 \times {e}^{2x} \times 2 = - 10 {e}^{2x}$

$y = - 3 \sin(2x) \\ y' = - 3 \cos(2x) \times 2 = - 6 \cos(2x)$

$y = 2 {e}^{2x} - 4 {e}^{ - 2x} \\ y' = 2 \times {e}^{2x} \times 2 - 4 {e}^{ - 2x} \times ( - 2) = 4 {e}^{2x} + 8 {e}^{ - 2x}$