Question

Найти у сложной функции!!! помогите пожалуйста!! 25 б!!​

Answer 1

Ответ:

1.

a)

$y' = - \sin( \frac{ {x}^{2} - 2}{x + 3} ) \times \frac{( {x}^{2} - 2)'(x + 3) - (x + 3)'( {x}^{2} - 2) }{ {(x + 3)}^{2} } = \\ = - \sin( \frac{ {x}^{2} - 2 }{x + 3} ) \times \frac{2x(x + 3) - ( {x}^{2} - 2) }{ {(x + 3)}^{2} } = \\ = - \sin( \frac{ {x}^{2} - 2 }{x + 3} ) \times \frac{2 {x}^{2} + 6x - {x}^{2} + 2 }{ {(x + 3)}^{2} } = \\ = - \sin( \frac{ {x}^{2} - 2 }{x + 3} ) \times \frac{ {x}^{2} + 6x + 2 }{ {(x + 3)}^{2} }$

б)

$y' = \frac{1}{4 {x}^{2} - 6x + 1} \times (4 {x}^{2} - 6x + 1)' = \\ = \frac{8x - 6}{4 {x}^{2} - 6x + 1}$

в)

$y' = ln(3) \times {3}^{6 {x}^{3} - 2 {x}^{2} - x} \times (18 {x}^{2} - 4x - 1)$

г)

$y' = - 4 {( {x}^{5} - 6 {x}^{4} + 2x)}^{ - 5} \times ( {x}^{5} - 6 {x}^{4} + 2x) '= \\ = - 4 \times \frac{ 5{x}^{4} - 24 {x}^{3} + 2 }{ {( {x}^{5} - 6 {x}^{4} + 2x)}^{5} } = \\ = \frac{ - 20 {x}^{4} + 96 {x}^{3} - 8}{ {( {x}^{5} - 6 {x}^{4} + 2x)}^{5} }$

2.

$y = y(x0) + y'(x0)(x - x0)$

$y = {x}^{4} - 6x + 2 \\ x0 = 2$

$y(x0) = y(2) = {2}^{4} - 6 \times 2 + 2 = \\ = 16 - 12 + 2 = 6$

$y' = 4 {x}^{3} - 6 \\ y'(x0) = y'(2) = 4 \times {2}^{3} - 6 = \\ = 32 - 6 = 26$

$y = 6 + 26(x - 2) = 6 + 26x - 52 \\ y = 26x - 46$