Force from pressure on a piece of matter in a star

Question

My physics book states that the force from pressure on a small piece of matter in a star can be written: $$dF_p=(P(r)-P(r+d r)) d A \approx-\frac{d P}{d r} d r d A$$ Where $r$ is the distance from the center. Where does the last approximation come from?

Answer 1

$$\frac{dP}{dr} = \lim_{\Delta r\to 0}\frac{P(r+\Delta r) - P(r)}{\Delta r} \approx \frac{P(r+\delta r) -P(\delta r)}{\delta r}$$ where $\delta r$ is small enough.

Hence $$P(r+\delta r) - P(r) \approx \delta r \frac{dP}{dr}$$

$$P(r) - P(r+\delta r) \approx -\delta r \frac{dP}{dr}$$