derivative derivative of tan(1/x)

解答

导数

\frac{d}{d x} (tan (\frac{1}{x}))

- \frac{sec ^{2} ( \frac{1}{x} )}{x ^{2}}

求解步骤

\frac{d}{d x} (tan (\frac{1}{x}))

使用连锁律:

sec^{2} (\frac{1}{x}) \frac{d}{d x} (\frac{1}{x})

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

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

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

化简

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

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

\frac{( cos ( 2 x ) )}{2}

(- 4, 4), (4, 4)

\frac{d}{d x} (\frac{x}{5})

e^{3 x}

\frac{d}{d x} y = sin (\frac{1}{x})