What is the d/(dt)(ln(-ln(1-t))) ?

The d/(dt)(ln(-ln(1-t))) is -1/(ln(1-t)(1-t))

What is the first d/(dt)(ln(-ln(1-t))) ?

The first d/(dt)(ln(-ln(1-t))) is -1/(ln(1-t)(1-t))

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial y} (4 x - y)

\int_{4}^{16} (3 x) d x

\frac{d}{d x} (\frac{( x - y )}{( x + y )})

\int x sin (\frac{x ^{2}}{2}) d x

\int \frac{2}{7 x} d x

What is the d/(dt)(ln(-ln(1-t))) ?
The d/(dt)(ln(-ln(1-t))) is -1/(ln(1-t)(1-t))
What is the first d/(dt)(ln(-ln(1-t))) ?
The first d/(dt)(ln(-ln(1-t))) is -1/(ln(1-t)(1-t))