Question

Найти производную функции
y=sqrt(arcctg(x/2))

Answer 1

Ответ:

$y = \sqrt{arcctg \frac{x}{2} }$

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