Determine dy/dt for y=11x^2+5x given x=10 and dx/dt=12

asked Sep 27, 2023 188k views

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Differentiate both sides with respect to
. By the chain rule,

$y = 11x^2 + 5x \implies (dy)/(dt) = 22x (dx)/(dt) + 5 \frac{dx]{dt}$

Given that
x=10 and
(dx)/(dt)=12 , we find

$(dy)/(dt) = 22*10*12 + 5*12 = \boxed{2700}$

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