derivative of (2x/(6x^2+1))

Lösung

\frac{d}{d x} (\frac{2 x}{6 x ^{2} + 1})

\frac{2 ( - 6 x ^{2} + 1 )}{( 6 x ^{2} + 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x}{6 x ^{2} + 1})

Entferne die Konstante:

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

= 2 \frac{d}{d x} (\frac{x}{6 x ^{2} + 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} ( 6 x ^{2} + 1 ) - \frac{d}{d x} ( 6 x ^{2} + 1 ) x}{( 6 x ^{2} + 1 ) ^{2}}

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

\frac{d}{d x} (6 x^{2} + 1) = 12 x

= 2 \cdot \frac{1 \cdot ( 6 x ^{2} + 1 ) - 12 xx}{( 6 x ^{2} + 1 ) ^{2}}

Vereinfache

2 \cdot \frac{1 \cdot ( 6 x ^{2} + 1 ) - 12 xx}{( 6 x ^{2} + 1 ) ^{2}} : \frac{2 ( - 6 x ^{2} + 1 )}{( 6 x ^{2} + 1 ) ^{2}}

= \frac{2 ( - 6 x ^{2} + 1 )}{( 6 x ^{2} + 1 ) ^{2}}