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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{0}^{3} (- x^{2} + x - 1) d x

\int_{1}^{16} \frac{1}{x} d x

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

\frac{d}{d x} (x^{12} ln (x))

\int \frac{16}{x ( x ^{2} + 4 ) ^{2}} d x

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