find the derivative of y = 2x²(3x - 4)

Explanation:

Step1: Expand the function

$$y = 2x^{2}(3x - 4)=6x^{3}-8x^{2}$$

Step2: Apply the power rule

The power rule is $\frac{d}{dx}(x^{n})=nx^{n - 1}$. For $y = 6x^{3}-8x^{2}$, the derivative $y^\prime$: For the term $6x^{3}$, using the power rule: $\frac{d}{dx}(6x^{3})=6\times3x^{3 - 1}=18x^{2}$ For the term $-8x^{2}$, using the power rule: $\frac{d}{dx}(-8x^{2})=-8\times2x^{2 - 1}=-16x$

Step3: Combine the derivatives of the terms

$$y^\prime=18x^{2}-16x$$

Answer:

$18x^{2}-16x$