Explicit upper and lower bounds on certain functions related to $\zeta(s)$ for $s>1$

We provide explicit upper and lower bounds for certain commonly occurring expressions that involve the Riemann zeta function $\zeta(s)$ and its derivatives on $s>1$.

For example, this improves upon existing bounds for $(s-1)\zeta(s)$ and its derivatives, and for $(\zeta'/\zeta)(s)$.