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Popular >

derivative of ln(1-ln(x))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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