7.
$$\mathrm { h } ( x ) = \frac { 2 } { x + 2 } + \frac { 4 } { x ^ { 2 } + 5 } - \frac { 18 } { \left( x ^ { 2 } + 5 \right) ( x + 2 ) } , \quad x \geqslant 0$$
- Show that \(\mathrm { h } ( x ) = \frac { 2 x } { x ^ { 2 } + 5 }\)
- Hence, or otherwise, find \(\mathrm { h } ^ { \prime } ( x )\) in its simplest form.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c78b0245-5c5a-407f-ad8a-602949a76e05-10_729_1235_644_351}
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\caption{Figure 2}
\end{figure}
Figure 2 shows a graph of the curve with equation \(y = \mathrm { h } ( x )\). - Calculate the range of \(\mathrm { h } ( x )\).