derivades

d_{x}[a^{x}] = e^{x}·ln(a)

d_{log_{a}(x)}[a^{log_{a}(x)}]·d_{x}[log_{a}(x)] = 1

e^{log_{a}(x)}·ln(a)·d_{x}[log_{a}(x)] = 1

e^{log_{a}(e^{ln(x)})}·ln(a)·d_{x}[log_{a}(x)] = 1

d_{x}[log_{a}(x)] = (1/x)^{log_{a}(e)}·(1/ln(a))

log_{a}(x) = ( 1/(ln(a)+(-1)) )·x^{(1+(-1)·log_{a}(e))}

a^{x} = e^{ln(a)·x}

1 = log_{a}(e)·ln(a)