derivative of (2x/(2x+1))

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

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

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

\frac{d x}{d x} = 1

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

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

Vereinfache

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

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

\int_{0}^{N} e^{(- s t)} sin (5 t) d t

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

\int \frac{1}{x - 1} d x

x \to 2 lim (2 - x^{2})

\int_{1}^{e^{4}} x^{4} ln (x) d x