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

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

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

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

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derivative of

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

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

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}{( 1 - x ) ^{2}}

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

Simplify

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

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

\frac{d}{d x} (x^{0.45})

\frac{\partial}{\partial x} (ln (x^{4} + y^{4}))

\int e^{t} sin (2 t) d t

y = 6 + 5 x^{2} - 2 x^{3}

\frac{d}{d x} (cos^{7} (2 x^{2} + 1))

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