试从 $\frac{\mathrm{d} x}{\mathrm{~d} y}=\frac{1}{y^{\prime}}$ 导出 $\frac{\mathrm{d}^2 x}{\mathrm{~d} y^2}=-\frac{y^{\prime \prime}}{\left(y^{\prime}\right)^3} ; \quad \frac{\mathrm{d}^3 x}{\mathrm{~d} y^3}=\frac{3\left(y^{\prime \prime}\right)^2-y^{\prime} y^{\prime \prime \prime}}{\left(y^{\prime}\right)^5}$ ．
(1) $y=x \ln x$;
(2) $y=\sin ^4 x+\cos ^4 x$;
(3) $y=\frac{x+3}{x^2-5 x+6}$.
$y=x^2 \sin 2 x$ ，求 $y^{(50)}$ ．
思考题：你能验证 $\left(x^{n-1} \mathrm{e}^{\frac{1}{x}}\right)^{(n)}=\frac{(-1)^n}{x^{n+1}} \mathrm{e}^{\frac{1}{x}}$ 吗？