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

The derivative of (ln(x)/(1-x)) is (1-x+xln(x))/(x(1-x)^2)

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

The first derivative of (ln(x)/(1-x)) is (1-x+xln(x))/(x(1-x)^2)

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

\frac{1 - x + x ln ( x )}{x ( 1 - x ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( ln ( x ) ) ( 1 - x ) - \frac{d}{d x} ( 1 - x ) ln ( x )}{( 1 - x ) ^{2}}

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

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

= \frac{\frac{1}{x} ( 1 - x ) - ( - 1 ) ln ( x )}{( 1 - x ) ^{2}}

Simplify

\frac{\frac{1}{x} ( 1 - x ) - ( - 1 ) ln ( x )}{( 1 - x ) ^{2}} : \frac{1 - x + x ln ( x )}{x ( 1 - x ) ^{2}}

= \frac{1 - x + x ln ( x )}{x ( 1 - x ) ^{2}}

y^{^{'}} = 2 + 3 y^{2}

\frac{d}{d x} ((\frac{x}{x + 1})^{2016})

\int \frac{1}{P - Z} + \frac{1}{Z} d Z

n = 1 \sum \infty \frac{3 n}{n !}

\int csc^{3} (x) \cdot sec (x) d x

What is the derivative of (ln(x)/(1-x)) ?
The derivative of (ln(x)/(1-x)) is (1-x+xln(x))/(x(1-x)^2)
What is the first derivative of (ln(x)/(1-x)) ?
The first derivative of (ln(x)/(1-x)) is (1-x+xln(x))/(x(1-x)^2)