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Popular >

derivative of ln(-ln(1-x))

Solution

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

Solution

- \frac{1}{ln ( 1 - x ) ( 1 - x )}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{- ln ( 1 - x )} \cdot \frac{1}{1 - x}

Simplify

\frac{1}{- ln ( 1 - x )} \cdot \frac{1}{1 - x} : - \frac{1}{ln ( 1 - x ) ( 1 - x )}

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

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of ln(-ln(1-x)) ?
The derivative of ln(-ln(1-x)) is -1/(ln(1-x)(1-x))
What is the first derivative of ln(-ln(1-x)) ?
The first derivative of ln(-ln(1-x)) is -1/(ln(1-x)(1-x))