I don't understand a step in my notes, about Taylor expansion

[fluidistic]

Homework Statement

$P_0 (t+dt)=P_0(t)(1-\gamma dt )$ (1)
Therefore $P_0 (t)+\frac{dP_0 (t)}{dt} \approx P_0 (t)-\gamma P_0(t)dt$. (2)
Where the approximation is due to a Taylor expansion apparently.

Homework Equations

Taylor expansion of f around $x_0$ : $f(x)\approx f(x_0)+\frac{df(x_0)}{dx}(x-x_0)$.

The Attempt at a Solution

Considering that (1) holds true, I do not understand the implication. In other words I don't understand why (2) is true.
I also do not understand the Taylor expansion used in equation (2). What is the point being expanded around?
Thanks for any help!

 

[Sourabh N]

From (1), they obtain an expression for the first derivative, using the definition of first derivative from the Taylor expanson. They then plug that in on the left hand side of (2) to obtain the right hand side.

Also, the function is expanded around the point $t$.

 

[fluidistic]

From (1), they obtain an expression for the first derivative, using the definition of first derivative from the Taylor expanson. They then plug that in on the left hand side of (2) to obtain the right hand side.

Also, the function is expanded around the point $t$.

Hi Sourab, thanks for helping me.
Edit: I got it! thanks a lot!