Derivative of Gamma Function at 1/Proof 1

Proof
From Reciprocal times Derivative of Gamma Function:


 * $\displaystyle \dfrac {\map {\Gamma'} z} {\map \Gamma z} = -\gamma + \sum_{n \mathop = 1}^\infty \paren {\frac 1 n - \frac 1 {z + n - 1} }$

Setting $n = 1$:

Using Gamma Function Extends Factorial:
 * $\map \Gamma 1 = \paren {1 - 1}! = 1$

Hence:
 * $\map {\Gamma'} 1 = -\gamma \map \Gamma 1 = -\gamma$