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

The derivative of ln(1/(1-x)) is 1/(1-x)

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

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

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

\frac{1}{1 - x}

Solution steps

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

Simplify

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

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

= \frac{1}{1 - x}

y = 4 x^{2}, y = x^{2} + 6

x \to 7 lim (x + 2)

\int x e^{x} ln (x - 1) d x

\int \frac{sin ^{5} ( ln ( x ) )}{x} d x

x \to 0 lim (\frac{5 + x - 5}{2 x})

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