Question

1.Найти производные функций
а) у=6х^5-7х^3+х-60
б) у=sinx-cos5x+tg(6x-9)
в) у=(х^3-7)/(2х+6)

Answer 1

Ответ:

А)

$y = 6 {x}^{5} - 7 {x}^{3} + x - 60 \\ {y}^{ '} = 6 \times 5 {x}^{5 - 1} - 7 \times {3x}^{3 - 1} + 1 = \\ 30 {x}^{4} - 21 {x}^{2} + 1$

Б)

$y = \sin(x) - \cos(5x) + \tan(6x - 9) \\ {y}^{'} = \cos(x) - ( - \sin(5x) \times 5) + \frac{1}{ { \cos }^{2} (6x - 9) } \times 6= \\ \cos(x) + 5 \sin(5x) + \frac{6}{ { \cos }^{2} (6x - 9)}$

В)

$y = \frac{ {x}^{3} - 7 }{2x + 6} \\ {y}^{'} = \frac{( {x}^{3} - 7)^{'} (2x + 6) - ( {x}^{3} - 7) {(2x + 6)}^{'} }{ {(2x + 6)}^{2} } = \\ \frac{3 {x}^{2} \times (2x + 6) - ( {x}^{3} - 7) \times 2 }{ {(2x + 6)}^{2} } = \\ \frac{6 {x}^{3} + 18 {x}^{2} - 2 {x}^{3} + 14}{{(2x + 6)}^{2}} = \\ \frac{4 {x}^{3} + 18 {x}^{2} + 14}{{(2x + 6)}^{2}} = \\ \frac{2 {x}^{3} + 9 {x}^{2} + 7}{ {2(x + 3)}^{2} }$