Question

производная функция y=x^2-2x+1/x-x^3

Answer 1

y'=(x²-2x+1/x-x³)'=
=(x²-2x)'+(x^(-1))'-(x³)'=
=2х-2+( -1)*(x^(-2))- 3x²=
= -3x²+2x-2-(1/x²)

Answer 2

1) Если $y = x^{2} - 2x + \dfrac{1}{x} - x^{3}$

$y' = 2x - 2 - \dfrac{1}{x^{2}} - 3x^{2} = \dfrac{-3x^{4} + 2x^{3} - 2x^{2} - 1}{x^{2}}$

2) Если $y = \dfrac{x^{2} - 2x + 1}{x - x^{3}} = \dfrac{(x - 1)^{2}}{x(1 - x^{2})} = \dfrac{(x - 1)^{2}}{x (1 - x)(1 + x)} = -\dfrac{x - 1}{x(x + 1)} = \dfrac{1 - x}{x + x^{2}}$

$y' = \dfrac{-(x + x^{2}) - (1 - x)(1 + 2x)}{(x + x^{2})^{2}} = \dfrac{x^{2} - 2x - 1}{(x + x^{2})^{2}}$