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

Simplify

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

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

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

f (x) = (2 x - 2)^{4} (x^{2} + x + 1)^{5}

\frac{\partial}{\partial x} (5 y e^{x})

y = 6 x, (1, 6)

\int sin (x + 7) 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)