Investigation: Differentiation of Exponential Functions (HSC SSCE Mathematics Advanced): Flashcards

$e$

$e^x$

$2.71828$

$1$

Gradient of $y = a^x$ at $x = 0$

$a^x \times \lim_{h \to 0} \frac{a^h - 1}{h}$

Identical (coincide perfectly)

Constant factor (limit $\neq 1$)

Only base where limit = $1$, giving self-derivative property

Self-derivative property simplifies differential equations