Question

Найти производную функций

Answer 1

Ответ:

а)

$y' = 6x - 5$

б)

$y' = ( {x}^{2} - x)'( {x}^{3} + x) + ({x}^{2} - x)( {x}^{3} + x)' = \\ (2x - 1)( {x}^{3} + x) + ( {x}^{2} - x)(3 {x}^{2} + 1) = \\ 2{x}^{4} + 2 {x}^{2} - {x}^{3} - x + 3 {x}^{4} + {x}^{2} + 3 {x}^{3} - x = \\ 5 {x}^{4} + 2 {x}^{3} + 3 {x}^{2} - 2x$

в)

$y' = \frac{( {x}^{5} + {x}^{3} + x)'(x + 1) - (x + 1)'( {x}^{5} + {x}^{3} + x) }{ {(x + 1)}^{2} } = \\ \frac{(5 {x}^{4} + 3 {x}^{2} + 1)(x + 1) - 1 \times ( {x}^{5} + {x}^{3} + x) }{ {(x + 1)}^{2} } = \\ \frac{5 {x}^{5} + 5 {x}^{4} + 3 {x}^{3} + 3 {x}^{2} + x + 1 - {x}^{5} - {x}^{3} - x }{ {(x + 1)}^{2} } = \\ \frac{4 {x}^{5} + 5 {x}^{4} + 2 {x}^{3} + 3 {x}^{2} + 1}{ {(x + 1)}^{2} }$

г)

$y' = - 6 {x}^{2} + 18$