What is the derivative of velocity with respect to height?

Question

I have a question on fluid dynamics which requires to find the derivative of velocity wrt to height? It was solved by my teacher but I am not able to grasp the solution.
Here is the question: -
A tank is filled with water upto a height h. The top of the tank has an area of cross section A. Water is coming out through a circular hole of area A/3. Find the initial acceleration with which the top level of water is decreasing?
The solution given:-
Can someone explain the part where derivative is taken and velocity changes into acceleration.

Chaitanya Tarkunde · Answer

v1=dh/dt,
Hence, v1*(dv1/dh) =(dh/dt) *(dv1/dh)
=dv1/dt
=d^2(h)/dt^2=acceleration,
This is how we end up with acceleration term a.

Danny LeBeau · Answer

$a=dv/dt$
$a=(dv/dh)times( dh/dt)$  (Multiply and divide by dh or to say using chain rule)
$a=v(dv/dh)$

What is the derivative of velocity with respect to height?

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