Derivative of Exponential Function/Corollary 1

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Corollary to Derivative of Exponential Function

Let $\exp x$ be the exponential function.

Let $c \in \R$.

Then:

$D_x \left({\exp \left({c x}\right)}\right) = c \exp \left({c x}\right)$


Proof

\(\displaystyle \displaystyle D_x \left({\exp \left({c x}\right)}\right)\) \(=\) \(\displaystyle c D_{c x} \left({\exp \left({c x}\right)}\right)\) Derivative of Function of Constant Multiple
\(\displaystyle \) \(=\) \(\displaystyle c \exp \left({c x}\right)\) Derivative of Exponential Function

$\blacksquare$