Exponential is Strictly Increasing/Proof 2
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Theorem
- The function $\map f x = \exp x$ is strictly increasing.
Proof
For all $x \in \R$:
| \(\ds D_x \exp x\) | \(=\) | \(\ds \exp x\) | Derivative of Exponential Function | |||||||||||
| \(\ds \) | \(>\) | \(\ds 0\) | Exponential of Real Number is Strictly Positive |
Hence the result, from Derivative of Monotone Function.
$\blacksquare$