Question

Вычислить производную функции

Answer 1

Ответ:

$y' = \frac{ \frac{1}{4} {(2x - 1)}^{ - \frac{3}{4} } \times 2(3 {x}^{2} + 6x - 1) - (6x + 6) \sqrt[4]{2x - 1} }{ {(3 {x}^{2} + 6x - 1) }^{2} } = \\ = \frac{ \frac{3 {x}^{2} + 6x - 1}{2 \sqrt[4]{ {(2x - 1)}^{3} } } - (6x + 6) \sqrt[4]{(2x - 1)} }{ {(3 {x}^{2} + 6x - 1) }^{2} } = \\ = \frac{1}{2 \sqrt[4]{ {(2x - 1)}^{3} }(3 {x}^{2} + 6x - 1) } - \frac{(6x + 6) \sqrt[4]{2x - 1} }{ {(3 {x}^{2} + 6x - 1)}^{2} }$