derivative (2x-1)/(4x+8)

Lösung

ableitung von

\frac{2 x - 1}{4 x + 8}

\frac{5}{4 ( x + 2 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x - 1}{4 x + 8})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 2 x - 1 ) ( 4 x + 8 ) - \frac{d}{d x} ( 4 x + 8 ) ( 2 x - 1 )}{( 4 x + 8 ) ^{2}}

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

\frac{d}{d x} (4 x + 8) = 4

= \frac{2 ( 4 x + 8 ) - 4 ( 2 x - 1 )}{( 4 x + 8 ) ^{2}}

Vereinfache

\frac{2 ( 4 x + 8 ) - 4 ( 2 x - 1 )}{( 4 x + 8 ) ^{2}} : \frac{5}{4 ( x + 2 ) ^{2}}

= \frac{5}{4 ( x + 2 ) ^{2}}

\int \frac{ln ( x ^{4} )}{x} d x

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

\frac{d y}{d x} = a \cdot y

(e^{f (x)})^{'}

\frac{d}{d x} ((\frac{x ^{2} + 2 x}{x + 1})^{5})