e^x = 1/x x = ln(1/x) = - ln(x)
e^-x = x -x = ln(x)
x*e^x = 1 ln(x) = 0
x^1/x = 1/e x/ln(x) = -1
x^-1/x = (1/x)^(1/x) = e ^( ln(x)/-x) = 1