23. $f(x)=\left[\cos ^{2}\left(x^{2}+\pi\right)+\sin ^{2} x^{2}\right] \cos \left(x^{3}+2 x\right)$ The derivative is ( ).
(A) $\left[8 x \cos x^{2} \cdot \sin x^{2}\right] \cos \left(x^{3}+2 x\right)-\left[\cos ^{2}\left(x^{2}+\pi\right)\right.$ $\left.+\sin ^{2} x^{2}\right] \sin \left(x^{3}+2 x\right) \cdot\left(3 x^{2}+2\right)$
(B) $\left[-2 \cos \left(x^{2}+\pi\right) \cdot \sin \left(x^{2}+\pi\right)+2 \cos x^{2}\right.$
$$
\begin{array}{l}
\left.\cdot \sin x^{2}\right] \cos \left(x^{3}+2 x\right)-\left[\cos ^{2}\left(x^{2}+\pi\right)\right. \\
\left.+\sin ^{2} x^{2}\right] \sin \left(x^{3}+2 x\right) \cdot\left(3 x^{2}+2 x\right)
\end{array}
$$
(C) $2 \cos x^{2} \cdot \sin x^{2} \cdot 2 x-2 \sin x^{2} \cdot \cos x^{2}$
(D) $-\sin \left(x^{3}+2 x\right) \cdot\left(3 x^{2}+2\right)$
(E) *
23. (1).
\[
\begin{array}{l}
\because f(x)=\left[\cos ^{2}\left(x^{2}+\pi\right)+\sin ^{2} x^{2}\right] \cos \left(x^{3}+2 x\right) \\
=\left[\cos ^{2} x^{2}+\sin ^{2} x^{2}\right] \cos \left(x^{3}+2 x\right) \\
=\cos \left(x^{3}+2 x\right) \text {. } \\
\therefore f^{\prime}(x)=-\sin \left(x^{3}+2 x\right) \cdot\left(3 x^{2}+2\right) \text {. } \\
\end{array}
\]