$12.5 y=\sqrt[3]{x^{2}-1}\left(x^{4}-1\right)$. 

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$12.5 y=\sqrt[3]{x^{2}-1}\left(x^{4}-1\right)$.
12.5 Let's write the given function as $y=\left(x^{2}-1\right)^{\frac{1}{3}}\left(x^{4}-1\right)$, from which, using the product differentiation rule (12.3) and the table of derivatives, we find

$$
\begin{aligned}
y^{\prime} & =\frac{1}{3}\left(x^{2}-1\right)^{-\frac{2}{3}} \cdot 2 x\left(x^{4}-1\right)+\left(x^{2}-1\right)^{\frac{1}{3}} \cdot 4 x^{3}= \\
& =\frac{2 x\left(x^{4}-1\right)}{3 \sqrt[3]{\left(x^{2}-1\right)^{2}}}+4 x^{3} \sqrt[3]{x^{2}-1}=\frac{2 x\left(x^{2}-1\right)\left(7 x^{2}+1\right)}{3 \sqrt[3]{\left(x^{2}-1\right)^{2}}}
\end{aligned}
$$