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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derivative of

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}

\int 2 e^{2 x - 1} d x

\frac{6 s + 7}{s ^{2} - s - 6}

\int \frac{1}{( 2 x + 1 ) ^{5}} d x

\int csc (5 x) cot (5 x) d x

\int_{2}^{5} \frac{5}{x - 2} d x

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)