Part 1/5:

Understanding Differentiability in Mathematics

Mathematics often poses challenges, especially when it comes to understanding functions and their derivatives. In this article, we will explore the concept of differentiability, the notations associated with derivatives, and how to graph them effectively.

What is Differentiability?

Differentiability refers to the ability to take a derivative of a function at every point within its domain. In simpler terms, it is about determining the slope of the function at any given point. The derivative can be seen as a measure of how the function's output changes concerning its input.

To capture this formally, we define the derivative of a function ( f(x) ) as:

[

f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}

]