The derivative of an odd function is an :

Let $\mathrm{f}\left(\mathrm{x}\right)$ be an odd function , then $\mathrm{f}(-\mathrm{x})=-\mathrm{f}\left(\mathrm{x}\right)$

Differentiating, $$\begin{gathered} {\mathrm{f}}^{\mathrm{\prime }}(-\mathrm{x})(-1)=-{\mathrm{f}}^{\mathrm{\prime }}\left(\mathrm{x}\right)\Rightarrow {\mathrm{f}}^{\mathrm{\prime }}(-\mathrm{x})={\mathrm{f}}^{\mathrm{\prime }}\left(\mathrm{x}\right) \\ \therefore {\mathrm{f}}^{\mathrm{\prime }}\left(\mathrm{x}\right)\text{ is an even function } \end{gathered}$$