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

The derivative of sqrt(x/(1-x)) is 1/(2sqrt(x)(-x+1)^{3/2)}

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

The first derivative of sqrt(x/(1-x)) is 1/(2sqrt(x)(-x+1)^{3/2)}

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

\frac{1}{2 x ( - x + 1 ) ^{\frac{3}{2}}}

Solution steps

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

Apply the chain rule:

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

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

Simplify

\frac{1}{2 \frac{x}{1 - x}} \cdot \frac{1}{( 1 - x ) ^{2}} : \frac{1}{2 x ( - x + 1 ) ^{\frac{3}{2}}}

= \frac{1}{2 x ( - x + 1 ) ^{\frac{3}{2}}}

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

\frac{e ^{- 5 s}}{s ^{2} - 4 s + 13}

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

(1 + x) \frac{d y}{d x} = 4 y

x (x - 2) \frac{d y}{d x} + 2 y = 0

What is the derivative of sqrt(x/(1-x)) ?
The derivative of sqrt(x/(1-x)) is 1/(2sqrt(x)(-x+1)^{3/2)}
What is the first derivative of sqrt(x/(1-x)) ?
The first derivative of sqrt(x/(1-x)) is 1/(2sqrt(x)(-x+1)^{3/2)}