Question

If y = 2x^3 - 4x and dx/dt = 4, find dy/dt when x = 1.

Please show me how to solve this problem with steps.

Answer 1

first find dy/dx
dy/dx = 6x^2 - 4

then dy /dx for x = 1
dy/dx = 6(1)^2 - 4
dy/dx = 2

then apply chain rule

dy/dt = dy/dx * dx/dt

dy/dt = 2 * 4
dy/dt = 8

Answer 2

just differentiate with respect to t

dy/dt = 6x^2 dx/dt - 4 dx/dt
sub in dx/dt=4 and x=1

dy/dt = 6(1)(4) - 4(4)
= 24 - 16 = 8