Let $$\vartheta \left( u ight) = \sum_{- \infty}^\infty e^{- \pi n^2 u}$$ for $\Re{\left( u ight)} > 0$. We wish to show that $$\vartheta' \left( 1 ight) = - \frac{\vartheta \left( 1 ight)}{4}$$