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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\frac{d}{d x} (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}{x ^{2}}

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

Simplify

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

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

\int tan (x) sec^{2} (x) d x

\int \frac{1}{2} sin (\frac{2 π t}{5}) d t

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

\int \frac{8}{t ^{2} ( t ^{2} - 4 )} d t

x \to 2 lim (5 x^{2} - 4 x + 3)

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)