[tex]f(x) = \sqrt{(x - 1)(x - 3)} = \sqrt{ {x}^{2} - 4x + 3} \\ f'(x) = \frac{1}{2 \sqrt{ {x}^{2} - 4x + 3 } } \times (2x - 4) = \\ \frac{2(x - 2)}{2 \sqrt{ {x}^{2} - 4x + 3 } } = \frac{x - 2}{ \sqrt{ {x}^{2} - 4x + 3 } } \\ x_{o} = - 2 \\ f' = \frac{ - 2 - 2}{ \sqrt{( - 2) {}^{2} - 4 \times ( - 2) + 3} } = \\ \frac{ - 4}{ \sqrt{4 + 8 + 3} } = - \frac{ 4}{ \sqrt{15} } [/tex]

Ответ: е