Part 1/5:

Understanding the General Power Rule and Derivatives at x = 0

In this article, we will revisit the concept of the general power rule, specifically addressing what happens when (x) equals zero. This topic is important in calculus, as it helps clarify the behavior of functions under certain conditions, particularly the implications for derivatives when variables approach zero.

The General Power Rule Explained

At the core of the general power rule lies the function (Y = X^n), where (n) is a constant representing the power to which (X) is raised. The power rule states that the derivative of (Y) with respect to (X) can be found using the formula:

[

Y' = n \cdot X^{n-1}

]