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#1 2005-10-15 08:13:41

Registered: 2005-07-23
Posts: 11


How do you differentiate:

1 / ln x ????????????????????????????????????????????

98% of the teenage population does or has tried smoking pot. If you're one of the 2% who hasn't, copy & paste this into your signature.


#2 2005-10-15 08:40:02

Registered: 2005-06-22
Posts: 4,900

Re: Differentiation

The quotient rule says that (u/v)' = (vu' - uv')/v², where u' and v' are the differentials of u and v with respect to x.

Taking u = 1 and v = ln x means that u' = 0 and v' = 1/x, so (u/v)' would be -1/x(ln x)².
There may be a simpler way of doing that that gives a simpler answer, but I'm sleepy so I can't see one.

Why did the vector cross the road?
It wanted to be normal.


#3 2005-11-07 22:41:07


Re: Differentiation

simpler way is probably using the chain rule. Take up logex to be (logex)^-1, then simply differentiate as normal:

-1(logex)^-2 x (1/x)

= -1/(x(logex)^2)

Sorry if my terminology isn't clear- im in australia and the syllabus is different here (just had my finals and im depressed over a poor effort in my most important exam...trying to find some solace by going over everything and brushing up my math skills...just can't believe how much effort i put in to make so many silly mistakes on the day...)

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