[tex]~~~~~~~~~y= 2x^3 -2x^2 -3x+1\\\\\\\implies \dfrac{dy}{dx} =\dfrac d{dx} \left( 2x^3 -2x^2 -3x +1\right)\\\\\\~~~~~~~~~~~=2 \dfrac{d}{dx}\left(x^3\right) - 2 \dfrac d{dx} \left(x^2\right) - 3 \dfrac d{dx} (x) +\dfrac{d}{dx}(1)\\ \\\\~~~~~~~~~~~=2\cdot 3x^2 -2\cdot 2x-3 +0~~~~~~~;\left [ \dfrac d{dx} x^n = nx^{n-1}\right]\\\\\\~~~~~~~~~~~=6x^2 -4x -3[/tex]
[tex]\text{The derivative is}~6x^2 -4x -3[/tex]
