I want to understand this equation - Fluid Mechanics

[Alexanddros81]

Hi all!
I have started reading Fluid Mechanics at my own pace (no university study)
and really I would like to grasp the ideas behind it.

So I have Fluid Mechanics by Cengel - 4th edition.
At page 45 the coefficient of compressibility or bulk modulus of elasticity (κ) is introduced.

$κ = V(\frac {\partial P} {\partial V})_T = ρ(\frac {\partial P} {\partial ρ})_T$ (Pa) (2-12)

It can also be expressed approximately in terms of finite changes as

$κ = - \frac {ΔP} {ΔV/V} = \frac {ΔP} {Δρ/ρ}$ (T = constant) (2-13)

I want to understand equation (2-12) and how it gets equation (2-13).
Obviously I would need to revise partial derivatives.
What else would I need to Know in order to understand these equations?
Your insight would be appreciated.

 

[Chestermiller]

Eqns. 13 is the finite difference approximation to Eqn. 2-12. Do you know how to approximate derivatives of a function using finite differences?

 

[Alexanddros81]

Eqns. 13 is the finite difference approximation to Eqn. 2-12. Do you know how to approximate derivatives of a function using finite differences?

I don't know. What should I be looking at?

 

[Chestermiller]

I don't know. What should I be looking at?

What is the definition of the derivative of f(x) with respect to x?