differentiate y = 12x^{-2} - 24x^{-3} 24x^{-1} 6x^{-3} - 24x^{-1}

$differentiate y = 12x^{-2} - 24x^{-3} 24x^{-1} 6x^{-3} - 24x^{-1}$

The power rule states that if $ y = ax^n $, then $ y^\prime=anx^{n - 1} $. For $ y = 12x^{-2} $, $ a = 12 $ and $ n=-2 $.

Substitute $ a = 12 $ and $ n=-2 $ into the power - rule formula: $ y^\prime=12\times(-2)x^{-2 - 1}=-24x^{-3} $.

$-24x^{-3}$ (the green - colored option)