найти производную функции:[tex]y = \frac{(x+1)^{2} }{x^{2} +2x}[/tex]. Created by way51. algebra-ru

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way51 @way51

July 2022 1 8 Report

найти производную функции:[tex]y = \frac{(x+1)^{2} }{x^{2} +2x}[/tex]

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ElectroM17

y = $\frac{(x+1)^2}{x^2+2x}$

y' = $(\frac{(x+1)^2}{x^2+2x})' = \frac{((x+1)^2)' * (x^2+2x) + (x+1)^2 * (x^2+2x)'}{x^2+2x} = \frac{(2x+2)*(x^2+2x)+(x^2+2x+1)*(2x+2)}{x^2+2x} = \frac{2x^3+4x^2+2x^2+4x+2x^3+4x^2+2x+2x^2+4x+2}{x^2+2x} = \frac{4x^3+12x^2+10x+2}{x^2+2x} = 4x^3+12+5+2 = 4x^3+19$

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