Part 2/7:
The relationship among these variables is encapsulated in the formula:
[
dy = f'(x) \cdot dx
]
Here, ( dy ) is dependent on ( dx ), emphasizing that any change in ( y ) relies on the small changes in ( x ). When ( dx ) is not equal to zero, this relationship allows us to express the derivative as:
[
\frac{dy}{dx} = f'(x)
]
Thus, differentiating serves as the mathematical foundation for understanding changes within a function and visualizing these shifts geometrically.