Question

помогите с математикой пожалуйста 4 примера

Answer 1

Ответ:

1

$( \frac{5 - x}{x} )' = ( \frac{5}{x} - 1)' = (5 {x}^{ - 1} - 1)' = \\ = - 5 {x}^{ - 2} - 0 = - \frac{5}{ {x}^{2} }$

2

$( \frac{7x}{x + 1} ) '= \frac{(7x)'(x + 1) - (x + 1)' \times 7x}{ {(x + 1)}^{2} } = \\ = \frac{7(x + 1) - 7x}{ {(x + 1)}^{2} } = \frac{7x + 7 - 7x}{ {(x + 1)}^{2} } = \frac{7}{ {(x + 1)}^{2} }$

3

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

4

$y = 4 {x}^{3} + 1 \\ x_0 = 1$

$f(x) = y(x_0) + y'(x_0)(x - x_0)$

$y(1) = 4 + 1 = 5$

$y' = 12 {x}^{2}$

$y'(1) = 12$

$f(x) = 5 + 12(x - 1) = 5 + 12x - 12 = \\ = 12x - 7$

- уравнение касательной