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

The derivative of cos(pi/x) is (pisin(pi/x))/(x^2)

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

The first derivative of cos(pi/x) is (pisin(pi/x))/(x^2)

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\frac{d}{d x} (cos (\frac{π}{x}))

\frac{π sin ( \frac{π}{x} )}{x ^{2}}

Solution steps

\frac{d}{d x} (cos (\frac{π}{x}))

Apply the chain rule:

- sin (\frac{π}{x}) \frac{d}{d x} (\frac{π}{x})

= - sin (\frac{π}{x}) \frac{d}{d x} (\frac{π}{x})

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

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

Simplify

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

= \frac{π sin ( \frac{π}{x} )}{x ^{2}}

What is the derivative of cos(pi/x) ?
The derivative of cos(pi/x) is (pisin(pi/x))/(x^2)
What is the first derivative of cos(pi/x) ?
The first derivative of cos(pi/x) is (pisin(pi/x))/(x^2)