Solved: "Find the derivatives of the functions. f(x)=ln|ln⁡x|" - Plainmath

Khadija Wells

Answered question

2021-06-21

Find the derivatives of the functions.

f (x) = \ln | \ln x |

Answer & Explanation

ensojadasH

Skilled2021-06-22Added 100 answers

The function we want to differentiate is

f (x) = \ln | \ln x |

Recall the generalized rule for the derivative of a natural logarithm of an absolute value:

\frac{d}{d x} [\ln | u |] = \frac{1}{u} \frac{d u}{d x}

Now we get

f^{'} (x) = \frac{1}{\ln x} \frac{d}{d x} (\ln x)

Recall that

\frac{d}{d x} (\ln x) = \frac{1}{x}

Thus

f^{'} (x) = \frac{1}{\ln x} \frac{1}{x} = \frac{1}{x \ln x}

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