log x^n = n log x,
so the log-log graph is a line of slope n
NB 1: (0,0) in log-log space is (1,1) in linear; (0,0) in linear is (-infty, -infty) in log-log

log' x^n is n/x
…so the -proportional- change in x^n as x increases -decreases-
that is, the following points map to 2^n under x^n:
x: 1,2,4,8,…: points gaps increase: lattice on log line
x^2: 1,sq(2),2,2*sq(2),4,etc : half-way between 'em: half the above lattice (b/c grows at twice the rate in log space

log' e^x is 1 (duh): grows at constant -proportional- rate
  (it's a line in log-linear space)
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1/(1+x) ~= 1-x; division related to log' 1 = 1
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NB: you can't so easily see the higher derivatives in these log space (AFAICT)