221. Differentiate the function $y=\left(x^{2}+2\right)(2 x+1)$.
Solution. Method I. We will use Rule IV with $u=$ $=x^{2}+2, v=2 x+1$. We have

$$
\begin{gathered}
y^{\prime}=\left(x^{2}+2\right)^{\prime}(2 x+1)+(2 x+1)^{\prime}\left(x^{2}+2\right)=2 x(2 x+1)+2\left(x^{2}+2\right)= \\
=4 x^{2}+2 x+2 x^{2}+4=6 x^{2}+2 x+4
\end{gathered}
$$

Method II. First, we multiply the expressions in the parentheses, and then find the derivative:

$$
\left(\left(x^{2}+2\right)(2 x+1)\right)^{\prime}=\left(2 x^{3}+4 x+x^{2}+2\right)^{\prime}=6 x^{2}+4+2 x
$$

222-227. Find the derivatives of the following functions: