# If y=x^3+2x and dx/dt=5, how do you find dy/dt when x=2 ?

$\frac{\mathrm{dy}}{\mathrm{dt}} = 70$
By differentiating with respect to $t$,
$\frac{\mathrm{dy}}{\mathrm{dt}} = \frac{d}{\mathrm{dt}} \left({x}^{3} + 2 x\right) = \left(3 {x}^{2} + 2\right) \frac{\mathrm{dx}}{\mathrm{dt}}$
by plugging in $x = 2$ and $\frac{\mathrm{dx}}{\mathrm{dt}} = 5$,
$= \left[3 {\left(2\right)}^{2} + 2\right] \left(5\right) = 70$