Differentiate both sides with respect to [tex]t[/tex]. By the chain rule,
[tex]y = 11x^2 + 5x \implies \dfrac{dy}{dt} = 22x \dfrac{dx}{dt} + 5 \dfrac{dx]{dt}[/tex]
Given that [tex]x=10[/tex] and [tex]\frac{dx}{dt}=12[/tex], we find
[tex]\dfrac{dy}{dt} = 22\times10\times12 + 5\times12 = \boxed{2700}[/tex]
