Calculus with Applications (10th Edition)

The graphs seem to coincide, illustrating that $\displaystyle \frac{d}{dx}[e^{x}]=e^{x}$
On the same coordinate system, graph $f(x)=e^{x}$ and $y=\displaystyle \frac{f(x+h)-f(x)}{h}=\frac{e^{x+00001}-e^{x}}{0.0001}$ The two graphs seem to coincide. $h=0.0001$ is close to 0, so the graphs illustrate that for $f(x)=e^{x},$ $\displaystyle \lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}=f(x)$ that is, $\displaystyle \frac{d}{dx}[e^{x}]=e^{x}$