Derivative of Exponential Function/Corollary 3

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Corollary to Derivative of Exponential Function

Let $\exp x$ be the exponential function.


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


Proof

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

$\blacksquare$


Sources