Answer
$$-\frac{1}{2}$$
Work Step by Step
\begin{aligned}
&\text { The derivative is defined as}\\
&\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}=f^{\prime}(x)
\end{aligned}
\begin{array}{l}
\begin{aligned}
& \lim _{h \rightarrow 0} \frac{f(h-2)-f(-2)}{h}=f^{\prime}(-2) \\
=& \lim _{h \rightarrow 0} \frac{\frac{-2+h+2}{-2+h}-\frac{-2+2}{-2}}{h} \\
=& \lim _{h \rightarrow 0} \frac{\frac{h-2}{h}-0}{h} \\
=& \lim _{h \rightarrow 0} \frac{\frac{h}{h-2}}{h} \\
=& \lim _{h \rightarrow 0} \frac{h}{(h-2)h} \\
=& \lim _{h \rightarrow 0} \frac{1}{h-2} \\
=-\frac{1}{2}
\end{aligned}
\end{array}
