Calculus solvings and Differentiation

Differentiation is a process in calculus used to find the derivative of a function. The derivative represents the instantaneous rate of change of a function with respect to one of its variables. Geometrically, it gives the slope of the tangent line to the function's graph at any given point.

One of the fundamental rules of differentiation is the power rule:
If $f(x) = x^n$, then its derivative, denoted as $f'(x)$ or $\frac{dy}{dx}$, is given by:

$$\frac{d}{dx}(x^n) = nx^{n-1}$$

For example, if $f(x) = x^3$: