The equation of exchange and the inflation rate

The equation of exchange states the money stock times by the velocity of money equals price level times by real income. In other words:

MV=PY

In this equation, all these four variables are so closely related that it is hard to tell how a movement in one variable influences the other.
Let's take implicit derivatives with respect to M.

d(MV)/dM=d(PY)/dM
=> V+M*(dV/dM)=Y*(dP/dM)+P*(dY/dM)

It looks messy. Why not times both sides by dM?

V*dM+M*dV=Y*dP+P*dY

It still looks messy. Why not divide both sides by MV? Wait! Note MV=PY. Therefore, why not divide the left hand by MV and the right hand by PY? Those denominators are basically equal, so it does not change the result.

(V*dM+M*dV)/MV=(Y*dP+P*dY)/PY
=> dM/M+dV/V=dP/P+dY/Y

Aha, the rate of change in money stock plus the rate of change in velocity equals the rate of change in price level plus the rate of change in real income. If you want to know the percentage changes, then just time each term by one hundred.

Let's substitute lower case m, v, p, and y for the rates of changes in money stock, velocity, price level, and real income, respectively.

m+v=p+y

Solve the equation for p. Note that p is the rate of change in the price level or inflation rate.

p=m+v-y

The inflation rate is determined by the rate of change in money stock plus the rate of change in price level less real income.

An increase in money stock can cause inflation only if neither the velocity nor the real income falls.

Can you see a run-away inflation? I see about three percent of inflation in this measure. It is greater than the BLS CPI inflation rate but I measured the price level for all items in real income not only consumption goods. Anyways, it is very different from the story the actual inflation should be much higher and government must be hiding the stuff, isn't it?