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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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