Applying the Power Rule for Derivatives in Calculus

In calculus, the power rule is a fundamental technique for finding derivatives of functions. When taking the derivative of a function of the form $f(x) = x^n$, where $n$ is a constant, the power rule states that the derivative is $f'(x) = nx^{n-1}$. For example, if $f(x) = 3x^2$, then the derivative is $f'(x) = 2\cdot3x^{2-1} = 6x$. This rule simplifies the process of finding derivatives and is essential for understanding more complex concepts in calculus.