Question

найти производную функцию у-2х^4 / 1-х^2

Answer 1

Ответ:

$\displaystyle y=\frac{2x^4}{1-x^2}\ \ ,\ \ \qquad \boxed{\ \Big(\frac{u}{v}\Big)'=\frac{u'v-uv'}{v^2}\ }\\\\\\\\y'=\frac{8x^3\cdot (1-x^2)-2x^4\cdot (-2x)}{(1-x^2)^2}=\frac{8x^3-8x^5+4x^5}{(1-x^2)^2}=\frac{8x^3-4x^5}{(1-x^2)^2}=\frac{4x^3(2-x^2)}{(1-x^2)^2}$