220. Differentiate the function $y=2 x^{3}\left(x^{6}-1\right)$.
Solution. Method I. Using rule IV, we get

$$
\begin{aligned}
& \left(2 x^{3}\left(x^{6}-1\right)\right)^{\prime}=\left(2 x^{3}\right)^{\prime}\left(x^{6}-1\right)+\left(x^{6}-1\right)^{\prime} \cdot 2 x^{3}=6 x^{2}\left(x^{6}-1\right)+6 x^{5} \cdot 2 x^{3}= \\
& =6 x^{8}-6 x^{2}+12 x^{8}=18 x^{8}-6 x^{2}=6 x^{2}\left(3 x^{6}-1\right) .
\end{aligned}
$$

Method II. First, we transform the given function: $2 x^{3}\left(x^{6}-1\right)=2 x^{9}-2 x^{3}$. Then we get

$$
y^{\prime}=\left(2 x^{9}-2 x^{3}\right)^{\prime}=18 x^{8}-6 x^{2}=6 x^{2}\left(3 x^{6}-1\right)
$$