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设函数${y=y(x)}$由${\left.\left\{\begin{matrix}x=\ln\left(1+t^{2}\right)+1,\\y=2\arctan t-\left(t+1\right)^{2}\end{matrix}\right.\right.}$确定$,$求$\frac{\mathrm{d}y}{\mathrm{d}x},\frac{\mathrm{d}^{2}y}{\mathrm{d}x^{2}}.$
                        
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