Derivative of Square Function/Proof 2

Theorem

Let $f: \R \to \R$ be the square function:

$\forall x \in \R: \map f x = x^2$

Then the derivative of $f$ is given by:

$\map {f'} x = 2 x$

Proof

From Power Rule for Derivatives:

$\map {\dfrac \d {\d x} } {x^n} = n x^{n - 1}$

The result follows by setting $n = 2$.

$\blacksquare$