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

The derivative of arctan(x-pi/2) is 4/(4x^2-4pix+pi^2+4)

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

The first derivative of arctan(x-pi/2) is 4/(4x^2-4pix+pi^2+4)

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derivative of

arctan (x - \frac{π}{2})

\frac{4}{4 x ^{2} - 4 π x + π ^{2} + 4}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x - \frac{π}{2}) = 1

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

Simplify

\frac{1}{( x - \frac{π}{2} ) ^{2} + 1} \cdot 1 : \frac{4}{4 x ^{2} - 4 π x + π ^{2} + 4}

= \frac{4}{4 x ^{2} - 4 π x + π ^{2} + 4}

What is the derivative of arctan(x-pi/2) ?
The derivative of arctan(x-pi/2) is 4/(4x^2-4pix+pi^2+4)
What is the first derivative of arctan(x-pi/2) ?
The first derivative of arctan(x-pi/2) is 4/(4x^2-4pix+pi^2+4)