Question

Вычислите производные пж

Answer 1

Ответ:

$f(x)=\dfrac{x^2+2x}{2x-6}\ \ \ ,\qquad \boxed{\ \Big(\dfrac{u}{v}\Big)'=\dfrac{u'v-uv'}{v^2}\ }\\\\\\f'(x)=\dfrac{(2x+2)(2x-6)-2\, (x^2+2x)}{(2x-6)^2}=\dfrac{2x^2-8x-12-2x^2-4x}{(2x-6)^2}=\\\\\\=\dfrac{-12x-12}{(2x-6)^2}=-\dfrac{12\, (x+1)}{4\, (x-3)^2}=-\dfrac{3\, (x+1)}{(x-3)^2}$