# If $v_t=cv(u-d)$ is scaled to $v_t=v(u-d)$, then what does “scaling $t$ by $c$” apply to?

If $$v_t=cv(u-d)$$ is scaled to $$v_t=v(u-d)$$, then what does "scaling $$t$$ by $$c$$" apply to?

Particularly, this equation is advanced w.r.t. time $$t$$. But if one scaled it, then does it mean that e.g.

$$\frac{d}{dt}$$ is $$\frac{d}{d(t/c)}$$? Or also $$dt$$ would be $$d(t/c)$$?

And if one calculates $$v_t$$ over some interval, say $$t \in [a,b]$$, then would this mean that one scales this by taking $$t \in [a/c,b/c]$$? But the equation does not have $$t$$ other than as $$u(t), v(t)$$.