Question

Найти производную функции

Answer 1

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