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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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