Question

Найти производную y′ .

Answer 1

Ответ:

Находим по формуле:

$y' = ( \frac{U}{V} ) = \frac{U'V - V'U}{ {V}^{2} }$

$y = \frac{ {x}^{4} - 8 {x}^{2} }{2 \sqrt{ {( {x}^{2} - 4) }^{3} } } = \frac{ {x}^{4} - 8 {x}^{2} }{2 {( {x}^{2} - 4) }^{ \frac{3}{2} } }$

$y' = \frac{(4 {x}^{3} - 16x) \times 2 \sqrt{ {( {x}^{2} - 4)}^{3} } - 2 \times \frac{3}{2} {( {x}^{2} - 4)}^{ \frac{1}{2} } \times 2x \times ( {x}^{4} - 8 {x}^{2}) }{4 {( {x}^{2} - 4) }^{3} } = \frac{2(4 {x}^{3} - 16) \sqrt{ {( {x}^{2} - 4) }^{3} } - 6x \sqrt{ {x}^{2} - 4}( {x}^{4} - 8 {x}^{2} ) }{4 {( {x}^{2} - 4)}^{3} } = \frac{(4 {x}^{3} - 16) \sqrt{ {( {x}^{2} - 4) }^{3} } - 3x \sqrt{ {x}^{2} - 4}( {x}^{4} - 8 {x}^{2} ) }{2 {( {x}^{2} - 4)}^{3} }$