Differentiation on Polynomials is Linear Operator

Theorem

Let $P \left({\R}\right)$ be the vector space of all polynomial functions on the real number line $\R$.

Then the differentiation operator $D$ on $P \left({\R}\right)$ is a linear operator.

Proof

Proved in Linear Combination of Derivatives.

$\blacksquare$

Sources

• Seth Warner: Modern Algebra (1965): $\S 28$: Example $28.6$