Question

2X^5
y=------------
X²-X
Найдите производные заданных функций

Answer 1

y=2x^5/[x(x-1)=2x^4/(x-1)
y`=[8x³(x-1)-1*2x^4]/(x-1)²=(8x^4-8x³-2x^4)/(x-1)²=(6x^4-8x³)/(x-1)²

Answer 2

$y = \dfrac{2x^5}{x^2 - x } \\ \\ \\ y = \dfrac{2x^5}{x(x-1)} \\ \\ \\ y = \dfrac{2x^4}{x - 1} \\ \\ \\ y' = \dfrac{(2x^4)'(x - 1) - 2x^4(x - 1)'}{ x - 1} = \dfrac{8x^3(x - 1) - 2x^4}{(x - 1)^2} = \\ \\ \dfrac{8x^4 - 8x^3 - 2x^4}{(x - 1)^2} = \dfrac{6x^4 - 8x^3 }{(x - 1)^2 }$