Найдите производную
[tex]y = - \frac{x {}^{2} + 2x}{x {}^{2} + 2x + 3 } [/tex]
[tex]y = - \frac{x {}^{2} + 2x}{x {}^{2} + 2x + 3 } [/tex]
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Ответ:
Пошаговое объяснение:
(u/v)'=u'v-uv' /v^2, y'= -( (2x+2)(x^2+2x+3)-(x^2+2x)(2x+2)) /(x^2+2x+3)^2=
-(2x^3+4x^2+6x+2x^2+4x+6-(2x^3+2x^2+4x^2+4x)) /(x^2+2x+3)^2= -(2x^3+6x^2+10x+6-2x^3-6x^2-4x) /(x^2+2x+3)^2=-(6x+6)/(x^2+2x+3)^2=-6x-6 /(x^2+2x+3)