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Popular Calculus >

derivative of f(x)=arctan(pi/x)

Solution

derivative of

f (x) = arctan (\frac{π}{x})

Solution

- \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}}

Graph

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Frequently Asked Questions (FAQ)

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