Question

Вычеслить производную!!

Answer 1

$y=2(x-2)sqrt{1+e^{x}}- 2lnfrac{sqrt{1+e^{x}}-1}{sqrt{1+e^{x}}+1} ; ;\\y'=2sqrt{1+e^{x}}+2(x-2)cdot frac{e^{x}}{2sqrt{1+e^{x}}} -\\-2cdot frac{sqrt{1+e^{x}}+1}{sqrt{1+e^{x}}-1} cdot frac{frac{e^{x}}{2sqrt{1+e^{x}}}(sqrt{1+e^{x}}+1)-(sqrt{1+e^{x}}-1)cdot frac{e^{x}}{2sqrt{1+e^{x}}}}{(sqrt{1+e^{x}}+1)^2} =$

$=2sqrt{1+e^{x}}+frac{e^{x}}{sqrt{1+e^{x}}}(x-2-cdot frac{sqrt{1+e^{x}}+1-sqrt{1+e^{x}}+1}{1+e^{x}-1})=$

$=2sqrt{1+e^{x}}+frac{e^{x}}{sqrt{1+e^{x}}}(x-2-frac{2}{e^{x}}})$