Question

Найти производную функции

Answer 1

Ответ:

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