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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of (x+sin(y))

\int (x + sin (y)) d x

derivative of f(x)=2x^2-9 derivative of

f (x) = 2 x^{2} - 9

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\int (\frac{x}{6})^{n} d x

integral from 0 to ln(4) of e^x-e^{-4x}

\int_{0}^{l n (4)} e^{x} - e^{- 4 x} d x

y^{''}+3y^'+2y=e^{-t},y(0)=0,y^'(0)=1

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{- t}, y (0) = 0, y^{^{'}} (0) = 1

Frequently Asked Questions (FAQ)

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