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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.
