Example 8. $y=\cos \ln x$.

Translate the text above into English, keeping the original text's line breaks and format, and output the translation result directly. 

Example 8. $y=\cos \ln x$.
Solution. Let $y=\cos u, u=\ln x$. We find $y^{\prime}=-\sin \ln x \times$ $\times \frac{1}{x}=-\frac{\sin \ln x}{x}$