Parity#
Definition: Even Function
A real function \(f: \mathcal{D} \subseteq \mathbb{R} \to \mathbb{R}\) is even iff
\[ f(-x) = f(x) \qquad \forall x \in \mathcal{D} \]
Definition: Odd Function
A real function \(f: \mathcal{D} \subseteq \mathbb{R} \to \mathbb{R}\) is odd if
\[ f(-x) = -f(x) \qquad \forall x \in \mathcal{D} \]
Theorem: Derivatives of Odd and Even Functions
If an odd function is differentiable, then its derivative, is an even function.
If an even function is differentiable, then its derivative is an odd function.
Proof
TODO