Question

If y = 3x3 + 4x and dx dt = 3, find dy dt when x = 2.

Answer 1

$y = 3x^3 + 4x\ \Rightarrow\displaystyle\ \frac{dy}{dt} = 9x^2 \frac{dx}{dt} + 4\frac{dx}{dt} \Rightarrow \\ \\ \frac{dy}{dt} = 9(2)^2 (3) + 4(3) = 120$