# What is the derivative of ln(ln(x))???

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• Anonymous

your u will be the ln(x)

your du will be 1/x dx

Then you just plug and chug and it all comes out to equal

1/(xln(x))

think of this as the chain rule. Let's take the derivative of ln(u): it's u'/u, right?

If we used substitution and pretended that u=lnx, the original problem would look like ln(u).

we know the derivative of u. since u=lnx, u'=1/x.

ok so the derivative of ln(u)= u'/u = (1/x)/lnx = 1/(xlnx)

keep in mind that all values of x are the absolute value of x so it's really:

1/|x|ln|x|