Question

If y = 3x^3 – 2x and dx/dt=3, find dy/dt when x = –2. Give only the numerical answer. For example, if dy/dt = 4, type only 4.

Answer 1

Differentiate both sides with respect to \(t\):
\[\frac{\mathrm dy}{\mathrm dt}=9x^2\frac{\mathrm dx}{\mathrm dt}-2\frac{\mathrm dx}{\mathrm dt}=(9x^2-2)\frac{\mathrm dx}{\mathrm dt}\]Plug in all the known values and find \(\dfrac{\mathrm dy}{\mathrm dt}\).