I think this works, I used \phantom to create an invisible copy of the part of the line above.
$$
\begin{flalign*}
&y(100)' - ? \\
&y' = -\frac{1}{\sqrt{1 - (\sqrt{1-x^{2}})^{2}}} \cdot \frac{1}{2\sqrt{1-x^{2}}} \cdot (-2x) = \frac{1}{\sqrt{1 - 1 + x^{2}}} \cdot \frac{\cancel{2}x}{\cancel{2}\sqrt{1-x^{2}}} = \frac{1}{\sqrt{x^{2}}} \cdot \frac{{x}}{\sqrt{1-x^{2}}} \\
& \phantom{y'} = \frac{\cancel{x}}{\pm \cancel{x}\sqrt{1-x^{2}}} = \pm\frac{1}{\sqrt{1-x^{2}}}
\end{flalign*}
$$