When I proved derivation the exponential function expose with problem that have to use derivative of $e^x$ $$\frac{de^x}{dx} = \lim_{h\to 0}\frac{e^{x+h} -e^x}h=\lim_{h\to 0} e^x \frac{e^h-1}h =e^x \cdot \lim_{h\to 0} \frac{e^h-1}h$$
Calculate $\displaystyle\lim_{h\to 0} \frac{e^h-1}h$ but can’t use l’hopital theorem and Taylors theorem because use derivative of $e^x$ . Please help me to solve it.