# Derivative of delta sinh

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## Theorem

Let $p\in$ $C_{rd}$. If $-\mu p^2 \in \mathcal{R}$, then $$\sinh^{\Delta}_p = p\cosh_p,$$ where $\sinh_p$ denotes the $\Delta$-$\sinh_p$ function and $\cosh_p$ denotes the $\Delta$-$\cosh_p$.