Question

Помогите найти производную функции

Answer 1

$y=ln\, \frac{x^3(x^2+4)^4}{\sqrt{x(x-1)}}\; \; ,\quad (lnu)'=\frac{1}{u}\cdot u'\\\\y'=\frac{\sqrt{x(x-1)}}{x^3(x^2+4)^4}\cdot \Big (\frac{x^3(x^2+4)^4}{\sqrt{x(x-1)}}\Big )'=\\\\=\frac{\sqrt{x(x-1)}}{x^3(x^2+4)^4}\cdot \frac{1}{x(x-1)}\cdot \Big ((3x^2(x^2+4)^4+x^3\cdot 4(x^2+4)^3\cdot 2x)\cdot \sqrt{x(x-1)}-\\\\-x^3(x^2+4)^4\cdot \frac{1}{2\sqrt{x(x-1)}}\cdot (2x-1)\Big )$