= Solution
Use the inverse <Lorentz transformation>, with $\gamma_u=(1-u^2/c^2)^{-1/2}$:
$$
x=\gamma_u(x'+ut'),\qquad t=\gamma_u\left(t'+\frac{ux'}{c^2}\right).
$$
Taking differentials along the object's trajectory gives
$$
\boxed{w=\frac{dx}{dt}=\frac{v+u}{1+uv/c^2}.}
$$
This is the collinear <relativistic velocity addition> law. It concerns the <velocity> of one object measured in two frames. By contrast the rate of change of the distance between two objects in one <laboratory frame> can be as large as
$$
\boxed{\frac{dD}{dt}=2c,}
$$
attained by oppositely directed light signals; for massive objects it is approached but not attained. This is not an object's <speed> in the other's rest frame and cannot transmit a signal faster than $c$.
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