Pressure gradient in Jeans Lenght

[Daaavde]

All the demonstrations on Jeans instability start with:

$\rho g \ge \nabla P$

Then they substitute $\nabla P$ with $nkT/R$.

But from ideal gas law: $PV = nkT$, so $P = nkT/V = nkT/R^3$
(I'm not interested in proportionality factors, so let's not bother about $4/3 \pi$, ecc...)

Now, gradient of $P$, to me, means to derivate with respect to $R$.
Hence:

$\nabla P = nkT/R^4$ (again, not interested in proportionality factors)

So, here's the problem:

On demonstrations: $\nabla P = nkT/R$
To me: $\nabla P = nkT/R^4$

Obviously, it's plain I'm missing something, still i can't see what it is.

(I apologize for my poor scholastic english, I'm not native speaker)

 

[LightHero]

Thank you for your help. P.S.: I'm aware of the fact that \rho g \ge \nabla P is only a sufficient condition and not a necessary one, but this is not the question here.