Fun with "exotic" constants

If $\LARGE{ e }^{ \frac { 1 }{ 12 } -\zeta ^{ \prime }(-1) }=B\times A$

Where $A$ is the Glaisher-Kinkelin constant

and $B$ is a real number

find $B$

Notation : $\zeta ^{ \prime }$ denotes the derivative of the zeta function