y=1/(e^2x +1)^2 Найдите производную функции ... Created by irusi9na. algebra-ru

(e^2x +1)^2 Найдите производную функции...

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$y=\frac{1}{(e^{2x}+1)^2}\\\\\star \; \; (\frac{1}{u})'=-\frac{u'}{u^2}\; \; ,\; \; u=(e^{2x}+1)^2\; \star \\\\\star \; \; (u^2)'=2u\cdot u'\; \; ,\; \; u=e^{2x}+1\; \star \\\\y'=-\frac{2(e^{2x}+1)\cdot (e^{2x}+1)'}{(e^{2x}+1)^4}=-\frac{2(e^{2x}+1)\cdot e^{2x}\cdot 2}{(e^{2x}+1)^4}=-\frac{4e^{2x}}{(e^{2x}+1)^3}$

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