# How do you find the derivatives of #y=lnabs(cosx)#?

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To make y real,

Applying function of function of function rule,

when

when

In brief,

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#### Explanation:

We note that the function:

is defined in the intervals:

where

In the central interval

#ln abs (cosx) = ln(cosx)#

#d/(dx) ln abs (cosx) = d/(dx) ln(cosx) = -sinx/cosx = -tanx#

In any other interval we have:

but:

so that

In conclusion:

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