derivative of (e^{x/2}/(x+1))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d}{d x} (x + 1) = 1

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

Vereinfache

\frac{e ^{\frac{x}{2}} \frac{1}{2} ( x + 1 ) - 1 \cdot e ^{\frac{x}{2}}}{( x + 1 ) ^{2}} : \frac{e ^{\frac{x}{2}} x - e ^{\frac{x}{2}}}{2 ( x + 1 ) ^{2}}

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

\int_{1}^{4} \frac{6}{x ^{2}} d x

d er i v a t i v e (x - 1)^{2} e^{x}

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

d er i v a t i v e f (x) = (x) (3 x - 2)

\frac{d y}{d t} = 3 y + y^{6}, y (0) = 1