Решение
1) y=x^3-3x/(2x^4+1) , x=-1, x=2
y` = 3x² - [3*(2x⁴ + 1) - 3x*(8x³)] / (2x⁴ + 1)² =
= 3x² - (6x⁴ + 3 - 24x⁴)/(2x⁴ + 1) = 3x² - (3 - 18x⁴)/(2x⁴ + 1)² =
= 3*[x² + (6x⁴ - 1)/(2x⁴ + 1)²]
1) x = - 1
y`(-1) = 3*[(-1)² + (6*(-1)⁴ - 1)/(2*(-1)⁴ + 1)] = 3*(1 + 5/3) = 3 + 5 = 8
2) x = 2
y`(2) = 3*[2² + (6*2⁴ - 1)/(2*2⁴ + 1)] = 3*(4 + 95/33) = 12 + 95/11 =
= 227/11 = 20(7/11)