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
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Appendix: Table $1$: Derivatives
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Appendix: Table $1$: Derivatives