What is the derivative of arctan(1/(2x-1)) ?

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

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

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

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derivative of

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

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

Solution steps

\frac{d}{d x} (arctan (\frac{1}{2 x - 1}))

Apply the chain rule:

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

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

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

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

Simplify

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

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

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