To find the derivative of a function, we use a special formula called the limit definition.

It looks like this:

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

What this means is that the derivative tells us how quickly something is changing at a specific point.

It’s like figuring out the slope of a line that just touches the curve of the function at one point.

Different Types of Derivatives:

1. First Derivative:
   • This shows how fast a function is changing.
   • For example, if you have the function $f(x) = x^2$, its first derivative is $f'(x) = 2x$.
2. Second Derivative:
   • This tells us how the first derivative is changing.
   • For the same function $f(x) = x^2$, the second derivative is $f''(x) = 2$.

Grasping these ideas can help you understand how functions act and change more deeply!