Question

Пожалуйста помогитеее​

Answer 1

Ответ:

1.

$( \sin(x) + C) '= \cos(x)$

верно

2.

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

верно

3.

$(tgx + C)' = \frac{1}{ \cos {}^{2} (x) }$

верно

4.

$( \frac{ {x}^{4} }{4} +C )' = \frac{1}{4} \times4 {x}^{3} = {x}^{3}$

верно

5.

$(arctgx + C) '= \frac{1}{1 + {x}^{2} }$

верно

6.

$( \frac{a {}^{x} }{ ln(a) } +C )' = \frac{1}{ ln(a) } \times ln(a) \times a {}^{x} = a {}^{x}$

верно

7.

$( \frac{1}{a}arctg( \frac{x}{a} ) + C) '= \frac{1}{a} \times \frac{1}{1 + \frac{ {x}^{2} }{ {a}^{2} } } \times ( \frac{x}{a} )' = \\ = \frac{1}{a} \times \frac{ {a}^{2} }{x {}^{2} + {a}^{2} } \times \frac{1}{a} = \frac{1}{ {x}^{2} + {a}^{2} }$

верно