254. $f(x)=\ln ^{3}\left(x^{2}-1\right)$.

254. $f(x)=\ln ^{3}\left(x^{2}-1\right)$. 

The translation is the same as the original text because it is a mathematical expression which is universal and does not change when translated into English. However, if you meant to have the problem number and the function description translated, it would be:

254. $f(x)=\ln ^{3}\left(x^{2}-1\right)$.

254. $f(x)=\ln ^{3}\left(x^{2}-1\right)$. 

In this case, the text is already in a form that is commonly used in English mathematical literature.
Solution. We have $f(x)=\ln ^{3}\left(x^{2}-1\right)$. The order of intermediate functions is as follows: $f(x)=u^{3} ; u=\ln v ; v=x^{2}-1$. Therefore,

$$
f^{\prime}(x)=3 \ln ^{2}\left(x^{2}-1\right) \cdot \frac{1}{x^{2}-1} \cdot 2 x=\frac{6 x}{x^{2}-1} \ln ^{2}\left(x^{2}-1\right) .
$$