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**Jaswahhihi****Member**- Registered: 2005-07-23
- Posts: 11

How do you differentiate:

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

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

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.

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**Ash****Guest**

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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