derivada de la exponencial

d_{x}[e^{x}] = lim[h-->0][ (1/h)( e^{x+h}+(-1)·e^{x} ) ]
d_{x}[e^{x}] = e^{x}·lim[h-->0][ (1/h)( e^{h}+(-1) ) ]
d_{x}[e^{x}] = e^{x}·lim[h-->0][ (1/h)( (1+h+(1/2)·h^{2}+...(1/n!)·h^{n}+...)+(-1) ) ]
d_{x}[e^{x}] = e^{x}


d_{x}[a^{x}] = lim[h-->0][ (1/h)( a^{x+h}+(-1)·a^{x} ) ]
d_{x}[a^{x}] = a^{x}·lim[h-->0][ (1/h)( a^{h}+(-1) ) ]
d_{x}[a^{x}] = a^{x}·lim[h-->0][ (1/h)( e^{ln(a)·h}+(-1) ) ]
d_{x}[a^{x}] = a^{x}·lim[h-->0][ (1/h)( (1+(ln(a)·h)+(1/2)·(ln(a)·h)^{2}+...(1/n!)·(ln(a)·h)^{n}+...)+(-1) ) ]
d_{x}[a^{x}] = a^{x}·ln(a)