derivative ((2x+3))/((x^2+1))

Lösung

ableitung von

\frac{( 2 x + 3 )}{( x ^{2} + 1 )}

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

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x + 3}{x ^{2} + 1})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 2 x + 3 ) ( x ^{2} + 1 ) - \frac{d}{d x} ( x ^{2} + 1 ) ( 2 x + 3 )}{( x ^{2} + 1 ) ^{2}}

\frac{d}{d x} (2 x + 3) = 2

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

= \frac{2 ( x ^{2} + 1 ) - 2 x ( 2 x + 3 )}{( x ^{2} + 1 ) ^{2}}

Multipliziere aus

2 (x^{2} + 1) - 2 x (2 x + 3) : - 2 x^{2} - 6 x + 2

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