Tag Archive

amateur astronomy awk bash b[e] supergiant cartoon conference convert evolved star exoplanet fedora figaro fits fun galaxy iraf large magellanic cloud latex linux lmc machine learning magellanic clouds massive star matplotlib meteor mypaper paper peblo photometry planet pro-am pyraf python red supergiant scisoft skinakas observatory small magellanic cloud smc spectroscopy starlink talk ubuntu university of crete video x-ray yellow hypergiant

Derivatives of non natural logarithms and exponentials

Some useful calculations to keep in mind !!

> changing bases in logarithms: loga x = logb x / logb a
for base 10 and e: log x = ln x / ln 10
(log e = 1 / ln 10)

> derivative of exponential with other base:

d (ax) / dx = ax ln a

in the case of base 10: d (10x) / dx = 10x ln 10

> derivative of logarithm with other base:

d (loga x) / dx = d (ln x / ln a) / dx = 1 / ( x ln a)

so in the case of base 10: d (log x) / dx = 1 / ( x ln 10)

A useful online resource for calculations is Wolfram Alpha ‘s engine.