In literature I've studied that the probability density function of a random variable X is the derivative of probability distribution function.
Mathematically speaking, it is the slope of the function. What is the significance? Am I missing something?
At every point $x$ where the PDF $f_X$ is continuous, the probability that $x-h\leqslant X\leqslant x+h$ is approximately $(2h)\cdot f_X(x)$ when $h>0$ is small.