Derivative of Function of Constant Multiple/Corollary

Corollary of 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:
 * $D_x \left({f \left({a x + b}\right)}\right) = a D_{a x + b} \left({f \left({a x + b}\right)}\right)$.

Proof
First we show $D_x \left({a x + b}\right) = a$:

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