Question

find the derivative of the function, y = x^2(4x^2 - 9x) y =

Explanation:

Step1: Expand the function

\( y = x^2(4x^2 - 9x) = 4x^4 - 9x^3 \)

Step2: Differentiate term by term

\( y' = \frac{d}{dx}(4x^4) - \frac{d}{dx}(9x^3) \)

Step3: Apply power rule

\( y' = 4 \cdot 4x^3 - 9 \cdot 3x^2 = 16x^3 - 27x^2 \)

Answer:

\( 16x^3 - 27x^2 \)