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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

y^{^{'}} + 35 y = 7

d er i v a t i v e - 2 t^{2} - 8 t + 9

x \to 6 - lim (\frac{x - 6}{∣ x - 6 ∣})

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

\int 4 x e^{- 2 x^{2}} d x