Using the change of base formula:
f(x) = log(x) / log(x1)
Via the quotient rule:
f ' (x) =[ log(x1) / x  log(x) / (x1) ] / (log(x1))^2
Using what you mention:
f(x) = y = log(base x1) of x
(x1)^y = (x1)^(log base x1 of x) yielding
(x1)^y = x Now taking the log of both sides:
y log (x1) = log (x)
y = log (x) / log (x1)
If you differentiate this expression, you will end up with an identical result to the above method. Therefore, I will venture to guess that exponentiating in this fashion is perfectly fine (at least in this scenario). Whether it is true in all scenarios or not... is a question that I cannot answer.
Last fiddled with by Primeinator on 20100711 at 22:28
