Derivative of Exponential Function/Corollary 1

From ProofWiki
Jump to navigation Jump to search

Corollary to Derivative of Exponential Function

Let $\exp x$ be the exponential function.

Let $a \in \R$.

Then:

$\map {\dfrac \d {\d x} } {\map \exp {a x} } = a \map \exp {a x}$


Proof

\(\ds \map {\dfrac \d {\d x} } {\map \exp {a x} }\) \(=\) \(\ds a \map {\dfrac \d {\map \d {a x} } } {\map \exp {a x} }\) Derivative of Function of Constant Multiple
\(\ds \) \(=\) \(\ds a \map \exp {a x}\) Derivative of Exponential Function

$\blacksquare$


Sources