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

$2.71828$

$1$

Gradient at $x = 0$

$e^x$

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

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

They coincide perfectly

It's $2^x$ times a constant factor

$0.1, 0.01, 0.001, 0.0001$

It's the only base where $f'(x) = f(x)$