Question

What is the derivative of Y=2x^3-2x^2-3x+1 with respect to x?​

Answer 1

`~~~~~~~~~y= 2x^3 -2x^2 -3x+1\\\\\\\implies (dy)/(dx) =\frac d{dx} \left( 2x^3 -2x^2 -3x +1\right)\\\\\\~~~~~~~~~~~=2 (d)/(dx)\left(x^3\right) - 2 \frac d{dx} \left(x^2\right) - 3 \frac d{dx} (x) +(d)/(dx)(1)\\ \\\\~~~~~~~~~~~=2\cdot 3x^2 -2\cdot 2x-3 +0~~~~~~~;\left [ \frac d{dx} x^n = nx^(n-1)\right]\\\\\\~~~~~~~~~~~=6x^2 -4x -3`

`\text{The derivative is}~6x^2 -4x -3`