What is expand ((1+e^x)(dy)/(dx))/x ?

The solution to expand ((1+e^x)(dy)/(dx))/x is ((dy)/(dx))/x+(e^x(dy)/(dx))/x

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expand ((1+e^x)(dy)/(dx))/x

expand

\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}

Solution steps

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

Expand

(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}

Apply the fraction rule:

\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}

What is expand ((1+e^x)(dy)/(dx))/x ?
The solution to expand ((1+e^x)(dy)/(dx))/x is ((dy)/(dx))/x+(e^x(dy)/(dx))/x