Question

Найти производную функции y=3-x/x³-27

Answer 1

y=3-x/x³-27 = 3 - 1/x² - 27 = -1/x² - 24 = -x⁻² - 24

y' = (-x⁻² - 24)' = -(-2)x⁻³ - 0 = 2/x³

Answer 2

y=(3-x)/(x³-27)=-(x-3)/((x-3)*(x²+3x+9))=-1/(x²+3x+9).

y'=(-1/(x²+3x+9)'=((-1)'*(x²+3x+9)-((-1)*(x²+3x+9)')/(x²+3x+9)²=

=(0*(x²+3x+9)+(2x+3))/(x²+3x+9)²=(2x+3)/(x²+3x+9)².