Question

Найти производную функции
y=(cosx-x^2)/(Inx-5)

Answer 1

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Answer 2

Ответ:

$\displaystyle y=\dfrac{cosx-x^2}{lnx-5}\ \ ,\ \ \ \ \boxed{\ \Big(\frac{u}{v}\Big)'=\dfrac{u'v-uv'}{v^2}\ \ }\\\\\\y'=\frac{(-sinx-2x)\cdot (lnx-5)-(cosx-x^2)\cdot \dfrac{1}{x}}{(lnx-5)^2}=\\\\\\=\frac{-x\, (sinx+2x)(lnx-5)-cosx+x^2}{x\, (lnx-5)^2}$