展开 ((1+e^x)(dy)/(dx))/x

解答

展开

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

\frac{\frac{d y}{d x}}{x} + \frac{e ^{x} \frac{d y}{d x}}{x}

求解步骤

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

乘开

(1 + e^{x}) \frac{d y}{d x} : \frac{d y}{d x} + e^{x} \frac{d y}{d x}

= \frac{\frac{d y}{d x} + e ^{x} \frac{d y}{d x}}{x}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{\frac{d y}{d x} + e ^{x} \frac{d y}{d x}}{x} = \frac{\frac{d y}{d x}}{x} + \frac{e ^{x} \frac{d y}{d x}}{x}

= \frac{\frac{d y}{d x}}{x} + \frac{e ^{x} \frac{d y}{d x}}{x}

(\frac{6 x}{7} + \frac{3}{10}) (\frac{6 x}{7} - \frac{3}{10})

\frac{π ^{3} y ^{4} + 2 y ^{2} + 2}{9 ( y ^{2} + 1 )}

(- \frac{3}{2}, - 2) y (9, \frac{3}{2})

- e^{- 0}