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Answer:
[tex]\dfrac{dy}{dt}=432[/tex]
Step-by-step explanation:
Differentiate [tex]y=4(x^2-4x)[/tex]:
[tex]\implies y=4x^2-16x[/tex]
[tex]\implies \dfrac{dy}{dx}=8x-16[/tex]
[tex]\textsf{Given}\quad\dfrac{dx}{dt}=9[/tex]
Therefore:
[tex]\begin{aligned}\dfrac{dy}{dt}&=\dfrac{dy}{dx} \times \dfrac{dx}{dt}\\\\\implies \dfrac{dy}{dt}& = (8x-16) \times 9\\\\& = 9(8x-16)\end{aligned}[/tex]
When [tex]x=8[/tex]:
[tex]\implies \dfrac{dy}{dt}=9(8(8)-16)[/tex]
[tex]\implies \dfrac{dy}{dt}=432[/tex]