Question

ПОМОГИТЕ ПОЖАЛУЙСТА ​

Answer 1

Ответ:

1)

$f(x) = {e}^{x} + 6x \: \: \: \: \: \: \: x_{0} = 1$

$f'(x) = {e}^{x} + 6$

$f'(x_{0}) = {e}^{0} + 6 = 1 + 6 = 7$

2)

$f(x) = \frac{1}{5} {x}^{5} - ln(x) \: \: \: \: \: \: \: x _{0} = 1$

$f'(x) = \frac{1}{5} \times 5 {x}^{4} - \frac{1}{x} = {x}^{4} - \frac{1}{x}$

$f'(x _{0}) = {1}^{4} - \frac{1}{1} = 1 - 1 = 0$

3)

$f(x) = \frac{ \sin(x) }{ {e}^{x} } \: \: \: \: \: \: \: x_{0} = 0$

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

$f'(x_{0}) = \frac{ \cos(0) \times {e}^{0} - \sin(0) \times {e}^{0} }{ {e}^{2 \times 0} } = \frac{1 \times 1 - 0 \times 1}{1} = \frac{1}{1} = 1$