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[latex]y=2(x-2)\sqrt{1+e^{x}}- 2ln\frac{\sqrt{1+e^{x}}-1}{\sqrt{1+e^{x}}+1} \; ;\\\\y'=2\sqrt{1+e^{x}}+2(x-2)\cdot \frac{e^{x}}{2\sqrt{1+e^{x}}} -\\\\-2\cdot \frac{\sqrt{1+e^{x}}+1}{\sqrt{1+e^{x}}-1} \cdot \frac{\frac{e^{x}}{2\sqrt{1+e^{x}}}(\sqrt{1+e^{x}}+1)-(\sqrt{1+e^{x}}-1)\cdot \frac{e^{x}}{2\sqrt{1+e^{x}}}}{(\sqrt{1+e^{x}}+1)^2} =[/latex] [latex]=2\sqrt{1+e^{x}}+\frac{e^{x}}{\sqrt{1+e^{x}}}(x-2-\cdot \frac{\sqrt{1+e^{x}}+1-\sqrt{1+e^{x}}+1}{1+e^{x}-1})=[/latex] [latex]=2\sqrt{1+e^{x}}+\frac{e^{x}}{\sqrt{1+e^{x}}}(x-2-\frac{2}{e^{x}}})[/latex]