Question

Вычислить производную

Answer 1

а)

$y' = - 3 {x}^{ - 2} + 5 \times \frac{1}{2} {x}^{ - \frac{1}{2} } - 12 {x}^{2} + 2 \times ( - 4) {x}^{ - 5} = \\ = - \frac{3}{ {x}^{2} } + \frac{5}{2 \sqrt{x} } - 12 {x}^{2} - \frac{8}{ {x}^{5} }$

б)

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