Найдите производную,срочно! 24 пример!. Created by flightlessbird. algebra-ru

Найдите производную,срочно! 24 пример!...

October 2021 2 39 Report

Найдите производную,срочно! 24 пример!

taisasnitko

$y=\Big (\frac{1+x^2}{1-x}\Big )^3\\\\y'=3\Big (\frac{1+x^2}{1-x}\Big )^2\cdot \Big (\frac{1+x^2}{1-x}\Big )'=3\Big (\frac{1+x^2}{1-x}\Big )^2\cdot \frac{2x(1-x)+(1+x^2)}{(1-x)^2}=\\\\=3\Big (\frac{1+x^2}{1-x}\Big )^2}\cdot \frac{-x^2+2x+1}{(1-x)^2}=\frac{3(1+x^2)(1+2x-x^2)}{(1-x)^4}$

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NNNLLL54

Verified answer

y'=3((1+x²)/(1-x))²·(2x(1-x)+(1+x²)) /(1-x)²=3((1+x²)/(1-x))²·(-x²+2x+1)/(1-x)²=

3(1+x²)²(-x²+2x+1) / (1-x)³.

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