Question

Найти производную y=(6x-12)(3+x) /5x

Answer 1

Ответ:

$\displaystale \boxed{\ \Big(\frac{u}{v}\Big)'=\frac{u'v-uv'}{v^2}\ }\\\\\\y=\dfrac{(6x-12)(3+x)}{5x}=\dfrac{6x^2+6x-36}{5x}\\\\\\y'=\dfrac{(12x+6)\cdot 5x-(6x^2+6x-36)\cdot 5}{25x^2}=\dfrac{60x^2+30x-30x^2-30x+180}{25x^2}=\\\\\\=\dfrac{30x^2+180}{25x^2}=\dfrac{6x^2+36}{5x^2}$