Derivative of Riemann zeta

Theorem

The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}z} \zeta(z) = -\displaystyle\sum_{k=2}^{\infty} \dfrac{\log(k)}{k^z},$$ where $\zeta$ denotes the Riemann zeta and $\log$ denotes the logarithm.