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

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

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

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

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\frac{d}{d x} (arctan (\frac{π}{x}))

- \frac{π}{π ^{2} + x ^{2}}

Solution steps

\frac{d}{d x} (arctan (\frac{π}{x}))

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{π}{π ^{2} + x ^{2}}

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