Ответ: 1) - 1/2

[tex]y = \ctg( \frac{x}{2} ) [/tex]

[tex]y ' = \frac{1}{2} \times ( - \frac{1}{ \sin {}^{2} ( \frac{x}{2} ) } ) = - \frac{1}{2 \sin {}^{2} ( \frac{x}{2} ) } [/tex]

[tex]y '(\pi) = - \frac{1}{2 \sin {}^{2} ( \frac{\pi}{2} ) } = - \frac{1}{ 2\times 1} = - \frac{1}{2} [/tex]