Question

Найти производную функции

Answer 1

$1)y = {( {x}^{3} - 4 {x}^{2}) }^{16} \\ {y}^{.} = 16 {( {x}^{3} - 4 {x}^{2}) }^{15} \times (3 {x}^{2} - 8x) = \\ = 16 {x}^{31} (x - 8) {(x - 4)}^{15} \\ \\ 2)y = \frac{ \sqrt{ {x}^{2} + 1} }{x} \\ {y}^{.} = \frac{ \frac{1}{2} {( {x}^{2} + 1) }^{ - \frac{1}{2} } 2 {x}^{2} - {( {x}^{2} + 1 )}^{ \frac{1}{2} } }{ {x}^{2} } = \\ = \frac{1}{ \sqrt{ {x}^{2} + 1 } } - \frac{ \sqrt{ {x}^{2} + 1 } }{ {x}^{2} } \\ \\ 3)y = {(cos3x + 6)}^{3} \\ {y}^{.} = 3 {(cos3x + 6)}^{2} \times ( - 3sin3x) = \\ = - 9sin3x {(cos3x + 6)}^{2} .$