derivative cos(pi/x)

解答

导数

cos (\frac{π}{x})

\frac{π sin ( \frac{π}{x} )}{x ^{2}}

求解步骤

\frac{d}{d x} (cos (\frac{π}{x}))

使用连锁律:

- 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}})

化简

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

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

\int \frac{y}{x} + 4 x d x

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