Derivative of Function of Constant Multiple/Corollary

Corollary to Derivative of Function of Constant Multiple
Let $f$ be a real function which is differentiable on $\R$. Let $a, b \in \R$ be constants.

Then:
 * $\map {D_x} {\map f {a x + b} } = a \, \map {D_{a x + b} } {\map f {a x + b} }$

Proof
First it is shown that $\map {D_x} {a x + b} = a$:

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