derivative of e^{1/x}-(e^{1/x}/x)

解答

\frac{d}{d x} (e^{\frac{1}{x}} - \frac{e ^{\frac{1}{x}}}{x})

\frac{e ^{\frac{1}{x}}}{x ^{3}}

求解步骤

\frac{d}{d x} (e^{\frac{1}{x}} - \frac{e ^{\frac{1}{x}}}{x})

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (\frac{e ^{\frac{1}{x}}}{x}) = \frac{- e ^{\frac{1}{x}} - e ^{\frac{1}{x}} x}{x ^{3}}

= - \frac{e ^{\frac{1}{x}}}{x ^{2}} - \frac{- e ^{\frac{1}{x}} - e ^{\frac{1}{x}} x}{x ^{3}}

化简

- \frac{e ^{\frac{1}{x}}}{x ^{2}} - \frac{- e ^{\frac{1}{x}} - e ^{\frac{1}{x}} x}{x ^{3}} : \frac{e ^{\frac{1}{x}}}{x ^{3}}

= \frac{e ^{\frac{1}{x}}}{x ^{3}}

\frac{d}{d x} (x^{3} + x^{5})

\int \frac{x}{2 - x ^{2}} d x

\frac{\partial}{\partial x} (\frac{x ^{2}}{x ^{2} + 1})

(\frac{f ( t )}{g ( t )})^{'}

\frac{d}{d x} (x e^{x^{2}} (x^{2} + 1)^{10})