# How do you get substitution to recognized a derivative?

I have a simple expression involving a derivative:

x[t_] = Q/T[t]; Simplify[Derivative[1][x][t] /. Q -> x T[t]] 

That produces:$$-\frac{x T'[t]}{T[t]}$$I have another relation: $$T=a^{-1}$$. When I make the substitution, I get this:

FullSimplify[-((x*Derivative[1][T][t])/T[t]) /. T[t] -> 1/a[t]] 

$$-x a[t] T'[t]$$

But what I want is this: $$-\frac{x a[t]}{a'[t]}$$I know I can force the issue with an additional substitution of $$T'[t]=a'[t]^{-1}$$, but it seems to me that I’ve already given Mathematica everything it needs to make that substitution on it’s own. How do I force MMa to recognize this kind of substitution in the derivative?