Question

Найдите производные функции

Answer 1

Ответ:

$1)\ \ y=x^2(x-3)\ \ ,\qquad \qquad (uv)'=u'v+uv'\\\\y'=2x(x-3)+x^2\cdot 1=3x^2-6x\\\\\\2)\ \ y=\dfrac{1+2x}{3-5x}\ \ ,\qquad \qquad \Big(\dfrac{u}{v}\Big)'=\dfrac{u'v-uv'}{v^2}\\\\y'=\dfrac{2\, (3-5x)-(1+2x)\cdot (-5)}{(3-5x)^2}=\dfrac{11}{(3-5x)^2}$