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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

z \to 0 lim ((2 z - 8)^{\frac{1}{3}})

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

y^{^{'}} = - 2 x tan (y), y (0) = \frac{π}{2}

\int \frac{( x + 3 ) ^{2}}{x + 2} d x

\frac{d}{d x} (tan (x) ln (x))

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