Power rule
The power rule is a fundamental concept in mathematics, particularly in Calculus, which states that if $f(x) = x^n$, then $f'(x) = nx^{n-1}$. This rule is used to differentiate functions of the form $x^n$, where $n$ is a real number. It is a crucial tool for finding the Derivative of a function, which is essential in understanding the behavior of Physical systems. The power rule is widely used in various fields, including Physics, Engineering, and Economics, to Predict outcomes and model real-world phenomena. For example, it is used to calculate the Surface area of Platonic solids and to understand the behavior of Electron shells in Atomic physics. The power rule is also closely related to the concept of Tangent spaces and Contour integration.