What is (\partial)/(\partial x)(ln(x/(1-x))) ?

The answer to (\partial)/(\partial x)(ln(x/(1-x))) is 1/(x(-x+1))

Popular >

(\partial)/(\partial x)(ln(x/(1-x)))

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{\partial}{\partial 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 )}

t sin (3 t)

\int (x^{10} - 5 x^{2})^{3} (x^{9} - x) d x

x y^{^{'}} + 2 y - 12 = 0

\frac{d}{d x} (ln (\frac{x ^{3}}{e ^{3 x}}))

What is (\partial)/(\partial x)(ln(x/(1-x))) ?
The answer to (\partial)/(\partial x)(ln(x/(1-x))) is 1/(x(-x+1))