\(\begin{array}{l}
\quad y = \dfrac{\sin x}{x} + \dfrac{x}{\sin x}\\
TXD: D = \Bbb R\backslash\left\{0;\dfrac{\pi}{2} + k\pi\ \Bigg|\ k\in\Bbb Z\right\}\\
\quad y' = \left(\dfrac{\sin x}{x}\right)' + \left(\dfrac{x}{\sin x}\right)'\\
\Leftrightarrow y' = \dfrac{(\sin x)'.x - x'.\sin x}{x^2} + \dfrac{x'.\sin x - (\sin x)'.x}{\sin^2x}\\
\Leftrightarrow y' = \dfrac{x\cos x - \sin x}{x^2} + \dfrac{\sin x - x\cos x}{\sin^2x}\\
\Leftrightarrow y' = (x\cos x - \sin x)\left(\dfrac{1}{x^2} - \dfrac{1}{\sin^2x}\right)\\
\Leftrightarrow y' = \dfrac{(x\cos x - \sin x)(\sin^2x - x^2)}{x^2\sin^2x}\\
\Leftrightarrow y' = \dfrac{(x\cos x- \sin x)(\sin x - x)(\sin x + x)}{x^2\sin^2x}
\end{array}\)
