Why eˣ is its own derivative

Drag the base a and the step h; watch when the difference-quotient curve coincides with aˣ.

base a2.000

step h0.500

\frac{a^{x+h}-a^{x}}{h}=a^{x}\cdot\frac{a^{h}-1}{h}

difference quotient ÷ function 0.8284

Related concept: The derivative