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